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The Pennsylvania State University

The Graduate School

Department of Chemistry

UNDERSTANDING THE PROPULSION AND ASSEMBLY OF AUTONOMOUS NANO-

AND MICROMOTORS POWERED BY CHEMICAL GRADIENTS AND ULTRASOUND

A Dissertation in

Chemistry

Wei Wang

 2013 Wei Wang

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

August of 2013

The dissertation of Wei Wang was reviewed and approved* by the following:

Thomas E. Mallouk Evan Pugh Professor of Materials Chemistry and Physics Dissertation Advisor Chair of Committee

Ayusman Sen Distinguished Professor of Chemistry

Christine Dolan Keating Professor of Chemistry

Tony Jun Huang Associate Professor of Engineering Science and Mechanics

Barbara J. Garrison Shapiro Professor of Chemistry Head of Chemistry Department

*Signatures are on file in the Graduate School

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ABSTRACT

Nano- and micromotors are a type of machines that turn energy into mechanical motion at the corresponding scales. Autonomous nano- and micromotors have attracted the attention of the scientific community since the initial discovery of the catalytically powered motion of Au-Pt bimetallic nanowires in hydrogen peroxide (H2O2) solution. This particular nanomotor system operates by a self-generated electric field (self-electrophoresis) through asymmetric surface catalytic reactions. However there are two challenges that greatly limit the use of such nanomotors in biological systems: low energy conversion efficiency and poor bio-compatibility of the fuel and the propulsion mechanism. The goal of my research projects is to address these challenges by modifying existing and discovering new nano- and micromotor systems.

Chapter 1 provides a general overview of the research field of nano- and micromotor, the challenges within this field, and a concise description of the research projects discussed in this dissertation.

Chapter 2 in this dissertation is dedicated to addressing the issue of the low energy conversion efficiency of the Au-Pt nanomotors, which is estimated to be on the order of 10-9.

Four stages of energy loss are identified. A 10-3 energy is lost due to the non-electrochemical

-3 decomposition of H2O2 at the Pt end of the Au-Pt motor, and another 10 energy loss can be partially attributed to the fast diffusion of protons. The electrophoretic propulsion mechanism is found to be intrinsically inefficient, contributing to another 10-3 energy loss, while the electroosmotic flow near the charged substrate further slows down the motor. Efforts are made to improve the energy efficiency. Replacing platinum with the less catalytically active ruthenium increases the energy efficiency, and confining the proton flux with a tubular structure is also a promising way to improve the energy efficiency of catalytic motors. These two modifications combined improved the energy efficiency of bimetallic nanomotors by a factor of 12. A numerical model based on COMSOL multi-physics package provides useful information, and is

discussed in more detail in Chapter 5. The energy efficiency of a few other nano- and micromotor systems is also discussed. A better understanding of the energy loss of nanomotor systems sheds light on future designs of more efficient nanomotors.

The dynamic interactions and particle assembly phenomena in the bimetallic catalytic nanomotor system are investigated in Chapter 3. Au-Pt nanomotors in H2O2 solutions were found to form doublets and triplets of staggered shapes. A combination of asymmetric pumping and electrostatic interactions between charged ionic clouds around the nanomotors is proposed to explain the binding between two bimetallic nanomotors and the staggered shapes of these doublets. The spontaneous rotation and disintegration of these doublets are attributed to an asymmetric distribution of forces. In addition, bimetallic nanomotors can attract charged microparticles to form close-packed aggregates through electrophoretic attraction. The electrophoretic migration of these charged tracer particles near nanomotors is found to agree qualitatively with simulation results. The effect of particles assembly on the motion of nanomotors is also characterized and discussed.

In Chapter 4 a new propulsion mechanism for autonomously moving metallic nanomotors is described and discussed. Ultrasonic standing waves operating in the MHz frequency range can be used to levitate, propel, rotate, align and assemble metal microrods (2-3

µm long and ~300 nm diameter) in water. A self-acoustophoresis mechanism based on the shape asymmetry of the metal nanowires is proposed to explain the axial propulsion of the rods.

Furthermore such acoustic nanomotors interact with HeLa cells and with polystyrene microspheres in different ways. The significant binding between metallic microrods and HeLa cells in an acoustic field is attributed to a combined effect of colloidal aggregation at high ionic strength and specific binding on the cell surface. When incubated with gold microrods, HeLa cells show substantial uptake of these gold rods, which remain active inside the cells when exposed to ultrasonic standing waves. The ultrasonically driven movement of the metal microrods

and their interactions with live cells open up the possibility of driving and controlling metallic nanomotors in biologically relevant media.

TABLE OF CONTENTS

List of Figures ...... viii

List of Tables ...... xiii

Acknowledgements ...... xiv

Chapter 1 Introduction ...... 1

References ...... 5

Chapter 2 Understanding the energy efficiency of the bimetallic catalytic nanomotors ...... 8

2.1 Introduction ...... 8 2.2 Experimental details ...... 10 2.2.1 Synthesis of nanorods and nanotubes ...... 10 2.2.2 Motor tracking ...... 12 2.2.3 Oxygen evolution experiment ...... 13 2.3 Self-Electrophoretic Catalytic Motors ...... 14 2.3.1 Calculating the overall energy efficiency ...... 14 2.3.2 Energy loss through fuel decomposition...... 17 2.3.3 Energy loss from inefficient electrochemical reactions ...... 18 2.3.4 Energy loss through inefficient propulsion mechanism ...... 23 2.3.5 Energy loss through opposite electro-osmotic flow near the charged substrate ...... 25 2.4 Catalytic Bubble Motors ...... 27 2.5 Helical Micromotors ...... 28 2.6 Conclusions ...... 30 2.7 References ...... 30

Chapter 3 Dynamic motor interactions and particle assembly driven by catalysis on the surface of bimetallic nanorods ...... 34

3.1 Introduction ...... 34 3.2 Interactions between autonomously moving nanomotors ...... 36 3.2.1 Key observations of nanomotor interactions ...... 36 3.2.2 Interaction mechanisms ...... 37 3.2.3 Doublet rotation and splitting ...... 41 3.2.4 Tracking analysis of nanomotor interactions ...... 44 3.3 Interactions between nanomotors and charged tracer microparticles ...... 45 3.3.1 Key observations and interaction mechanisms ...... 45 3.3.2 Tracking analysis of the migration of PS particles towards nanomotors ...... 49 3.3.3 Nanomotors as microtransporters ...... 53 3.4 Conclusions ...... 54 3.5 References ...... 55

Chapter 4 Ultrasonically driven metallic nanomotors ...... 58

4.1 Introduction ...... 58 4.2 Experimental details ...... 60

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4.2.1 Acoustic experiments ...... 60 4.2.2 Pulse mode acoustic experiments ...... 62 4.2.3 Particle synthesis and tracking ...... 63 4.2.4 Motor-cell interactions ...... 63 4.3 Results and discussions ...... 64 4.3.1 Spherical polystyrene particles in ultrasonic standing waves ...... 64 4.3.2 Metallic microrods ...... 66 4.3.3 Metallic spheres and polymeric rods ...... 72 4.3.4 Discussion of forces at work ...... 73 4.3.6 Mechanism of axial rod propulsion ...... 76 4.3.7 Ultrasound power and energy conversion efficiency of acoustic nanomotors ...... 79 4.4 Modulation of the speed of acoustic motors via external parameters ...... 80 4.4.1 Voltage modulation...... 80 4.4.2 Frequency modulation ...... 82 4.5 Interactions between acoustic motors and biological cells ...... 83 4.5.1 Background ...... 83 4.5.2 Interactions between acoustic nanomotors and polystyrene beads ...... 85 4.5.3 Interaction between acoustic motors and HeLa cells in a mixed suspension ...... 86 4.5.4 Interactions between acoustic motors and HeLa cells after incubation ...... 90 4.6 Conclusions ...... 94 4.7 References ...... 94

Chapter 5 Numerical modeling of self-electrophoretic motors with the COMSOL Multi- Physics program ...... 100

5.1 Introduction ...... 100 5.2 Basic concepts and assumptions used in current COMSOL models ...... 102 5.3 Calculating motor speed based on the electroosmotic flow speed ...... 105 5.4 Modeling details and results ...... 109 5.4.1 Modeling details ...... 109 5.4.2 Modeling results ...... 111 5.5 Conclusions ...... 120 5.6 References ...... 121

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LIST OF FIGURES

Figure 2-1. Illustration of the self-electrophoretic propulsion mechanism for a Au-Pt catalytic nanomotor. Red represents high proton concentration, and blue represents low. The electric field E points from the anode (Pt) end to the cathode. The white arrow indicates the direction of motion for the motor...... 15

Figure 2-2. Gas chromatographic measurements of O2 evolution rates from bimetallic motors: Au-Pt nanorods (left), Au-Ru nanorods (middle), and Au-Ru nanotubes (right). Error bars represent standard deviations from triplicate measurements...... 16

Figure 2-3. Numerical simulation to determine the contributions of diffusion, electromigration, and convection to proton transport. (a): Steady-state proton distribution around a Pt (top)-Au (bottom) catalytic nanomotor (3 μm long and 300 nm in diameter) with a surface flux of 7×10-6 mol/(m2∙s). Red and blue represent high and low proton concentration (units in legend: mol/m3). Arrows illustrate proton flux contributions (arrow lengths are not in exact proportion to the flux); (b): Proton fluxes from diffusion, electromigration and convection along the nanorod long axis across the center line (dashed line in (a)); (c): Proton fluxes perpendicular to the nanorod surface from the top half (Pt end, across the black line in (a)). In (b) and (c) fluxes were integrated over the respective cross-sections...... 20

Figure 2-4. Relationship between the proton diffusion coefficient (DH+) and the motor speed from numerical simulations. DH+0 is the experimental proton diffusion coefficient in water. In the model the DH+/DH+0 ratio was varied between 0.1 to 10...... 21

Figure 2-5. FESEM images of Au-Ru nanotubes. (a) side and (b) end-on view...... 22

Figure 2-6. Equivalent circuit of the nanomotor-solution system. The blue cylinder around the bimetallic nanorod represents the solution near its surface, which is represented as a resistor in the equivalent circuit on the right...... 23

Figure 2-7. A self-electrophoretic nanomotor generates an electric field in the direction of motion, which in turn induces electro-osmotic flow along the charged wall of the cell in the opposite direction...... 26

Figure 3-1. Interactions between self-electrophoretic nanomotors moving in the same and opposite directions. (a): Two nanomotors moving in the same direction can easily form a doublet, which starts to rotate. Such doublets can further attract a third nanomotor and form triplets. In rare cases two nanomotors can attract each other head-to-tail. (b): The interaction between two nanomotors moving in the opposite direction is typically much more short-lived and weak...... 37

Figure 3-2. Electric field strength along the long axis of the nanomotors at different relative positions of two nanomotors. The electric field distribution as a function of the distance away from the nanomotor(s) is plotted for an isolated nanomotor (black dots), two nanomotors moving in the same direction (red squares) and in opposite directions (orange circles). The electric field is normalized to the highest point for the case with a single nanorod to illustrate the relative magnitude. Positive electric fields induce electroosmotic flows (indicated by black arrows) moving upward in the figure, and negative electric field downward. The cartoon bimetallic nanomotors and

arrows indicating the directions of the motor motion are overlaid for illustrative purposes...... 39

Figure 3-3. Numerical simulation of the electrostatic interactions between two nanomotors at different relative positions. The coordinates on both x and y axes in the images are indicated in μm. These images are slices of the xz planes of 3D simulation results. Colors in the images represent the space charge density (ρe in Eqn. 5-2, in units of C/m3), with red being high and blue being low. Artistic renderings of Au-Pt nanomotors are superimposed over the simulation results for illustrative purposes, with Pt being silvery and gold being golden in color. Hollow arrows indicate the directions of the motors’ motion...... 41

Figure 3-4. The rotation and splitting of a doublet composed of two Au-Pt nanomotors. Pt is the silver colored segment on the top and gold is at the bottom. (a): Two nanomotors of different speeds (U) undergo speed change when they bind to form a doublet, therefore experiencing changes in drag forces (Fdrag). As a result the non- zero net force (Fnet) acting on either nanomotor creates a net torque that rotates the doublet to the side of the slower motor. Fprop is the propulsion force. (b): The effect of Brownian motion and propulsion force on the doublet. Fatt. is the combined attractive forces that pull nanorods together (van der Waals and pumping effect). kT represents the thermal energy that is responsible for the Brownian motion, and θ is the separation angle between the two nanorods. Depending on the relative magnitude of the propulsion force, drag force, Brownian motion and attractive forces, the doublet can maintain a stable circular path or split...... 43

Figure 3-5. Tracking results and analysis of the interactions between two Au-Pt nanomotors. (a): snapshot sequence of two nanomotors (white circle) binding together and splitting apart within 1 second. Attachment begins at 0.017s and the splitting begins at 0.825 s and finishes at 0.858 s. (b): Tracking results showing the trajectory of the two nanomotors. (c) The relative distance between the centers of the two nanomotors during the period of interaction. Inset in (c) shows the circular trajectory of the centers of the two nanomotors...... 44

Figure 3-6. Assembly of charged tracer microspheres on nanomotors. Charged microspheres are attracted to and eventually attach to the surface of the motors. Depending on the charge type of the microparticles, they can attach to the Pt end (negatively charged particles) or Au end (positively charged particles). This stacking process can continue until a close packed particle assembly is formed around the moving nanorod...... 47

Figure 3-7. Tracking results of the assembly of 3 polystyrene microspheres on a Au-Pt nanomotor. The black arrows indicate the points at which the spheres first attach to the nanomotor surface. I: Free motor; II: motor + bead1; III: motor + bead2; IV: motor + bead3...... 50

Figure 3-8. The speed of nanomotor-PS aggregate with different numbers of microspheres attached on the motor surface. Two samples of aggregates were analyzed. Error bars reflect the standard deviation of the aggregate speed measured by manual tracking...... 51

Figure 3-9. Electrophoretic speed of a tracer PS particle as it approaches the nanomotor. Inset: numerical simulation of the electrical potential distribution of a Pt-Au nanomotor. Red and blue shading represent the electrical potential with red being positive and blue being negative, respectively. The arrows indicate the electric field. The electrophoretic speed of a PS particle with a zeta potential of -64 mV along the black dashed line is simulated and plotted as the blue curve (normalized to the peak speed). Red data points are from the tracking results of the first PS particle in Fig. 3- 7 (and are normalized to the peak speed). The effect of Brownian motion was subtracted from the velocity profile...... 52

Figure 4-1. Cylindrical ultrasonic cell. The transducer was mounted on a steel plate at the bottom of the cell. Inset: Illustration of the cell cross-section when the acoustic field is applied. The particles are shown in the levitation plane. The cell height, h, is defined as the distance between the top cover slip and the bottom wall of the cell...... 61

Figure 4-2. An illustration of the parameters used in the pulsed-mode ...... 62

Figure 4-3. Typical patterns formed by polystyrene (PS) tracer particles in the nodal plane in a 3.7 MHz acoustic field. (a)-(c) are ring patterns, streak patterns and a dense aggregate formed by 470 nm diameter PS particles, respectively. (d)-(f) are the same types of patterns formed by 2 μm diameter PS particles. In these dark field images, the particles appear bright and the background is dark. (g) Cartoons showing the dimensions of the formed patterns as well as the nodes...... 65

Figure 4-4. (a)-(c): Illustration of the kinds of motion (axial directional motion, in-plane rotation, chain assembly and axial spinning and pattern formation, especially ring patterns) of metal micro-rods in a 3.7 MHz acoustic field. AuRu rods (gold-silvery color in dark field) showed similar behavior to the Au rods, except that they moved with their Ru ends (the silvery end in the image) forward and aligned head-to-tail into chains. (d) and (e): Dark field images of typical chain structures and ring patterns formed by Au and AuRu rods. Note that the cartoons superimposed on (d) are intended to show the alignment of the rods and are not to scale or in proportion to the aspect ratio of the Au or AuRu rods...... 67

Figure 4-5. Illustration of chain assembly and directional motion of metal rods along the chains: (a) two metal rods moving in the same direction along the ring interacts and form a spinning doublet. (b) two metal rods moving in opposite directions either brush against each other or meet each other head-to-head; (c) when a metal microrod meets a chain moving in the opposite direction, the rod brushes against the chain and the two parties continue separately...... 71

Figure 4-6. Illustration of the forces experienced by a metal rod in an acoustic field during self-assembly into chains. Red and yellow colors denote forces that bring the rods closer and push them apart, respectively. Fz: the primary radiation force in the z direction; G: the gravitational force; Fp: the propulsion force; Fhydro: the hydrodynamic force from the vortex; Fe: the electrostatic force; Fxy: the transverse component of the primary radiation force in the levitation plane; FB: the Bjerknes force; FVW: the van der Waals force...... 74

Figure 4-7. Electron micrographs of Au (a) and AuRu (b) rods used in the ultrasonic propulsion experiments. For AuRu rods, the Au end is clearly concave and there is

also some incidence of rod branching at the Au end. The Ru end is usually pointed or flat. Au rods typically have one concave end and one pointed or flat end...... 78

Figure 4-8. The speed of acoustic nanomotors at various frequencies...... 82

Figure 4-9. Interaction between acoustic motors and 10 μm PS beads. The acoustic nanomotor (light grey, bottom left at 0 s) collides with a PS bead and changes its trajectory (moving to the right at 0.3 s). Scale bar: 10 μm. Images were taken in bright field...... 86

Figure 4-10. Binding between acoustic nanomotors and HeLa cells in a mixed suspension in an acoustic field...... 88

Figure 5-1. Illustration of the definition of s and L for a rod-shaped nanomotor...... 106

Figure 5-2. Fluid speed and its weight along the nanorod length. Fluid speed in the z direction was simulated by the COMSOL 2D model. α/<α> was calculated for each point, and a higher α/<α> value means a heavier weighting that the fluid speed carries at this point towards the final motor speed. The colored bimetallic rod is overlaid onto the figure for illustrative purpose. Negative values of fluid speed indicate a flow direction from the anode to the cathode. The simulation was carried out on a nanomotor with a surface zeta potential of -50 mV and flux of 7×10-6 mol/(m2∙s). The motor speed is calculated to be 21.6 μm/s...... 107

Figure 5-3. 2D model configuration of the bimetallic nanomotor system being simulated. The nanorod is placed in a square box of 100 μm on each side...... 112

Figure 5-4. Proton concentration distribution of a Au-Pt nanomotor. Pt is at the top. Bottom axis: r coordinates in μm. Legend: Proton concentration in mol/m3...... 112

Figure 5-5. Proton concentration along the cut line in Fig. 5-2 through the nanorod at various surface fluxes (units in mol/(m2·s)). An image of a AuPt nanorod is overlaid for reference. The units for x axis are μm. Pt is on the left...... 113

Figure 5-6. Electric potential profile of Au-Pt. Pt is on the top. Bottom axis: r coordinates in μm. Color legend: Proton concentration in mol/m3...... 114

Figure 5-7. Electric potential along the cut line in Fig. 5-4 through the nanorod at various surface fluxes (units in mol/(m2·s)). An image of a AuPt nanorod is overlaid for reference. The units for the x axis are μm. Pt is on the left...... 114

Figure 5-8. Fluid flow around a Au-Pt nanomotor. Color indicates the magnitude of the fluid flow in the z direction, and arrows indicate the directions of the fluid flow. The length of the arrow is normalized and does not represent the flow magnitude in the first image, while in the second image the arrow length is proportional to the flow magnitude. Pt is at the top. Bottom axis: r coordinates in μm. Color legend: Fluid flow velocity in the z direction in μm/s. Surface flux: 7×10-6 mol/(m2∙s) ...... 115

Figure 5-9. Motor speed and electrical potential difference ( ) between the anode and the cathode at various surface fluxes. Note: motor speed was calculated based on the fluid speed with the technique discussed in section 5.3...... 116

xii

Figure 5-10. 3D model configuration of the tubular nanomotor system. Inset: blow-up of the tubular shape of the nanomotor used in the simulation...... 117

Figure 5-11. y-z cut plane of the 3D simulation result of a tubular nanomotor showing the proton concentration profile inside and outside the tube. The flux inside the tube was set to be 1/10 of the outside flux to account for reduced mass transfer of H2O2 inside the tube. Both axis coordinates are in μm...... 117

Figure 5-12. Electric potential (red is high potential and blue is low potential) and electric field distribution for a tubular bimetallic nanomotor at a flux of 2×10-6 mol/m2·s on the outside surface and 2×10-7 mol/m2·s on the inside surface. Arrows indicate the electric field direction with the arrow length being proportional (right) to the field strength or normalized (left)...... 118

xiii

LIST OF TABLES

Table 4-1. Summary of behaviors of different samples in an acoustic field ...... 72

Table 5-1. 2D and 3D modeling parameters ...... 119

Table 5-2. Variables for COMSOL models ...... 119

xiv

ACKNOWLEDGEMENTS

I would like to start by thanking my advisor, Professor Mallouk, or what he insisted me calling him at the end of my first year here, Tom, for being a fantastic advisor. I might still be able to get a Ph.D. somewhere else, but my experience would not have been as nearly memorable and satisfying. I’ve more than once thought about what these 5 years would mean to my life, other than getting a degree, and I’ve come to realize that the things I learned the most are how to do science and do it right. I owe it for the most part to Tom. In addition, Tom has taught me how to be a great scientist and fun person at the same time. I will never forget his guitar, songs and great sense of humor.

My parents and my whole family back in China have been very supportive during my graduate career. Not only have they been very supportive ever since I expressed the interest in coming to the U.S. for graduate study, they have also stood behind me for every major decisions I have made, even when such decisions were not necessarily what they had hoped for. I’m extremely proud of being raised in such a loving family, and I take pride in giving back everything I have and will have to them in every possible way.

I’ve had the good fortune to be able to work closely with some of the best minds in the world. My committee members Dr. Sen, Dr. Keating and Dr. Huang, as well as Dr. Crespi, Dr.

Velegol, Dr. Mayer and Dr. Butler have been tremendously helpful throughout my graduate career with various projects I have worked on. I have also enjoyed my collaboration with Dr.

Mauricio Hoyos at Paris Tech (and his grad student Angelica) and Dr. Lamar Mair at NIST. I would have made very little, if any, research progress if I had not been listening to, discussing with, learning from and working with these brilliant people and their students. I would like to especially thank Dr. Yang Wang, who taught me all I needed to be ready for my project, and who has been such a good friend over the years even after she graduated.

Penn State has been a great place to live, learn and do research at. I would like to thank the department of chemistry for offering me the opportunity in 2008 to enjoy everything that has happened in the last five years. I owe a big thank you to all the staff members at Nanofab, MCL and all the other facilities that I have had the opportunity to work with. I would like to thank my advisor Tom as well as MRSEC for being generous with my financial aid even when I’m not being particularly productive, as well as all the research money I have spent on equipment and chemicals. Sorry a lot of things I bought turned out to be not as useful as I wanted them to be.

The Mallouk group has been a great family, and everyone has been particularly nice and helpful to me. I will certainly miss everyone very very much.

I would like to thank all my friends, now and in the past, in the U.S. and back in China, for all the great memories we have had together. A special thank-you to those who have been or still are part of the motor research group at Penn State, especially Suzanne Ahmed, Wentao Duan,

Tso-Yi Chiang, Sixing Li, Dr. Mike Ibele and Dr. Sam Sengupta, who have helped me greatly with my research. Getting a Ph.D. has not been easy, and I am extremely grateful that I was not fighting alone. I wish all the best to everyone.

Finally my blessing goes to my girlfriend. May she get better soon and be happy every day.

Chapter 1

Introduction

In 1959 physicist Richard Feynman gave the now famous lecture “There is plenty of room at the bottom”, in which he envisioned great prospects in exploring the world at the nanoscale and possibilities therein.1 This vision sparked a great deal of imagination and scientific and engineering endeavors in the years that followed. Nanomachines, often pictured and called nanorobots, have been and are still one of the most pursued fantasies among scientists and engineers as well as the general public.2-5

As the name implies, nanomotors are motors at the nanometer scale, or with one dimension loosely associated with that size regime. A nanomotor is an essential component of any nanomachine, being responsible for converting energy into mechanical motion. There are many biological examples of nano- and micromotors. For example, the human body is the host of countless tiny nanomotors in the form of proteins such as kinesin and myosin, which are responsible for the intracellular transport of cargos and muscle contraction, respectively, extracting energy from the conversion of ATP to ADP. Many types of bacteria such as

Escherichia coli are also micromotors, being propelled by rotating the flagella or cilia attached to their bodies.

Synthetic nanomotors, on the other hand, are relatively new.3, 6-8 The general goal of research in this field is to induce motion, preferentially autonomous motion, of molecules, particles or other small scale (nanometer to micrometer scale) objects of interest. When compared to natural nanomotors, their synthetic counterparts usually have much lower energy efficiency,9 stricter operating conditions,9 and limited uses.10-17 Nevertheless, research on artificial nanomotors and micromotors sheds light on many important questions that otherwise are difficult

to investigate, such as the fundamental principles of motion, energy transduction and signal communication at small scale, schooling effects of small and autonomously moving objects, among others. Moreover the study of artificial nanomotors may further our understanding of biological motors and cells, and lead to promising biomedical applications such as drug delivery and minimally invasive surgery. Therefore it is a rewarding and exciting research area that has attracted a great deal of interest, especially over the last decade.

Although it is a relatively young research field, the study of nanomotors and micromotors

(as well as pumps) has created a large pool of literature. In terms of the sizes of the synthesized motors, reports range from molecular nanomotors as small as a few nanomotors,6, 7 “buckycars” and motor proteins that are a few to tens of nm,18, 19 to catalytic nanomotors that are a few micrometers long,8, 20, 21 and all the way to macroscopic motors that operate in a totally different

Reynolds number regime and by different mechanisms. And speaking of mechanisms, a myriad of them have been exploited to propel motors of various sizes. For extremely small motors such as molecular motors, external stimuli are typically applied, and configuration changes rather than motion of the molecules usually follows.6, 7 Chemical fuels are a popular source of energy for a great number of motor systems covering a wide range, including enzymes and catalysts that show enhanced diffusion, 22-24 bimetallic nanorods that demonstrate self-electrophoretic motion in

8, 25 20, 26 H2O2, metallic tubes that show fast motion in H2O2 as a result of bubble recoil, and oil droplets or solid particles that move by surface tension gradients (the Marangoni effect).27-29

External fields such as magnetic and electric fields have also been used to propel nano/micro motors and pumps.16, 30-36

Amidst the optimistic expectations of nanomotors and the translation of research results to applications, a number of issues exist that unfortunately limit the practical utility of the current generation of nanomotors in biological environments. To start with, many catalytic nano/micromotor systems rely on the use of toxic hydrogen peroxide (H2O2) or hydrazine derivatives as the fuel.9, 14, 20, 37-44 Although there are reports that take advantage of bio-compatible

fuels such as glucose45 and bio-inspired mechanisms such enzymatic propulsion,24, 46, 47 they all have their own limitations that prevent these systems from being actually useful, at least at the current stage of development. In addition, the high ionic strength of biological fluids is incompatible with propulsion mechanisms based on electrophoresis and diffusiophoresis,9, 30, 31, 35,

38, 40, 46, 48 effectively eliminating these mechanisms from being used for biomedical applications unless they are improved in some way to circumvent this issue. Thirdly most of the existing mechanisms suffer from extremely low energy efficiency35, 36, 49-51. As will be discussed in more detail in Chapter 2, the energy efficiency of bimetallic nanomotors driven by self-electrophoresis is on the order of 10-8~10-9, and that of microjets propelled by bubbles is on the order of 10-10.

Although there are ways to improve the energy efficiency, much of the energy loss comes from the propulsion mechanism that is intrinsic to the motor system. While external electric and magnetic fields can be used to drive micro-objects in biological media, the resulting motion is not autonomous. Given the current strong interest in microrobotics for medical diagnostics, drug delivery, and minimally invasive surgeries, there continues to be a need for a bio-compatible energy transduction mechanism that can power autonomous micromotors.2, 52, 53

In this dissertation I describe and discuss my work to address some of the aforementioned issues commonly encountered in nano/micromotor research, in the hope of building the next generation of nano/micromotors propelled by self-generated fields that are potentially suitable for bio-medical applications. The first half of this dissertation focuses on bimetallic catalytic nanomotors propelled by self-electrophoresis in H2O2 solutions. In chapter 2 the low energy efficiency of this nanomotor system is investigated as a model for understanding the energy loss.

Four stages of energy loss are identified, and the energy efficiency is increased by a factor of 12 through a number of improvements. The energy efficiency of other micromotor systems is also discussed for comparison. In chapter 3 the dynamic interactions between and assembly of bimetallic catalytic nanomotors is presented. Such nanomotors are found to bind to each other and form doublets of staggered shapes. In addition, when mixed with non-catalytic charged tracer

particles self-assembly into close-packed aggregates is achieved. These interactions are found to be electric in nature.

In chapter 4 the focus is shifted to a new way to propel micromotors, namely MHz ultrasonic standing wave propulsion. I demonstrate that ultrasonic standing waves in the MHz frequency range can levitate, propel, rotate, align and assemble metallic micro-rods (2 µm long and 330 nm diameter) in water as well as in solutions of high ionic strength. A self- acoustophoresis mechanism based on the shape asymmetry of the metallic rods is proposed to explain this axial propulsion. In addition the potential of the recently discovered ultrasonically propelled metallic nanomotor is further exploited in the context of biological applications. The relationship between experimental parameters such as ultrasonic frequency and acoustic power and motor behaviors are investigated. Incubation of metal nanomotors with HeLa cells leads to cell uptake of microrods, and these microrods remain acoustically active inside the HeLa cells.

This leads to prospective bio-medical applications as well as tools for studying the intracellular environment and motor-organelle interactions.

In Chapter 5 a numerical simulation model of bimetallic nanomotors operating by self- electrophoresis is described. This simulation model is based on previous reports by Posner and coworkers,54, 55 and is built with COMSOL commercial simulation package. However modifications and simplification were employed in order to establish a model that is easier to understand and less computationally demanding, yet relatively accurate. The details of and typical results from this model (2D and 3D) are also listed in this chapter for reference. The establishment of this numerical simulation model of bimetallic nanomotors enables a wide range of simulation studies of this nanomotor system, including energy efficiency, scaling analysis and others.

References

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42. Campuzano, S.; Orozco, J.; Kagan, D.; Guix, M.; Gao, W.; Sattayasamitsathit, S.; Claussen, J. C.; Merkoçi, A.; Wang, J., Bacterial Isolation by Lectin-Modified Microengines. Nano Lett 2011, 12 (1), 396-401. 43. Balasubramanian, S.; Kagan, D.; Jack Hu, C.-M.; Campuzano, S.; Lobo-Castañon, M. J.; Lim, N.; Kang, D. Y.; Zimmerman, M.; Zhang, L.; Wang, J., Micromachine-Enabled Capture and Isolation of Cancer Cells in Complex Media. Angew. Chem. Int. Ed. 2011, 50 (18), 4161-4164. 44. Burdick, J.; Laocharoensuk, R.; Wheat, P. M.; Posner, J. D.; Wang, J., Synthetic Nanomotors in Microchannel Networks: Directional Microchip Motion and Controlled Manipulation of Cargo. J Am Chem Soc 2008, 130 (26), 8164-8165. 45. Mano, N.; Heller, A., Bioelectrochemical Propulsion. J Am Chem Soc 2005, 127 (33), 11574-11575. 46. Pantarotto, D.; Browne, W. R.; Feringa, B. L., Autonomous propulsion of carbon nanotubes powered by a multienzyme ensemble. Chem Commun (Camb) 2008, (13), 1533-5. 47. Sanchez, S.; Solovev, A. A.; Mei, Y. F.; Schmidt, O. G., Dynamics of Biocatalytic Microengines Mediated by Variable Friction Control. J. Am. Chem. Soc. 2010, 132 (38), 13144- 13145. 48. Howse, J. R.; Jones, R. A. L.; Ryan, A. J.; Gough, T.; Vafabakhsh, R.; Golestanian, R., Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk. Phys. Rev. Lett. 2007, 99 (4), 048102. 49. Paxton, W. F.; Sen, A.; Mallouk, T. E., Motility of catalytic nanoparticles through self- generated forces. Chemistry-a European Journal 2005, 11 (22), 6462-6470. 50. Sabass, B.; Seifert, U., Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer. J. Chem. Phys. 2012, 136 (6). 51. Sabass, B.; Seifert, U., Efficiency of Surface-Driven Motion: Nanoswimmers Beat Microswimmers. Phys. Rev. Lett. 2010, 105 (21). 52. Mirkovic, T.; Zacharia, N. S.; Scholes, G. D.; Ozin, G. A., Fuel for Thought: Chemically Powered Nanomotors Out-Swim Nature’s Flagellated Bacteria. ACS Nano 2010, 4 (4), 1782-1789. 53. Ebbens, S. J.; Howse, J. R., In pursuit of propulsion at the nanoscale. Soft Matter 2010, 6 (4), 726. 54. Moran, J. L.; Posner, J. D., Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis. J. Fluid Mech. 2011, 680, 31-66. 55. Moran, J. L.; Wheat, P. M.; Posner, J. D., Locomotion of electrocatalytic nanomotors due to reaction induced charge autoelectrophoresis. Phys Rev E 2010, 81 (6).

Chapter 2 Understanding the energy efficiency of the bimetallic catalytic nanomotors

2.1 Introduction

Nano- and microscale motors are tiny objects that are capable of converting the energy of chemical fuels or external fields into mechanical motion.1, 2 Such motors are ubiquitous in the biological world, ranging from enzymatic assemblies that are nanometers in size to bacteria and cells that are in the range of micrometers to tens of micrometers. Synthetic motors that are similar in size to bacteria were first introduced in 2004-2005.3,4 The first generation of these motors were

2-3 micron long bimetallic rods (Pt-Au and Ni-Au) that catalytically decomposed hydrogen peroxide to oxygen and water and moved at speeds in the range of 10 µm/s. Over the past decade, bimetallic catalytic motors have been re-designed for faster movement5-9 and for functionality that includes sensing, pumping and cargo delivery.10-13 Microjets are a related class of tubular or conical catalytic motors that also catalyze hydrogen peroxide decomposition.14-21 Unlike smaller nanorod motors, which are propelled by self-electrophoretic forces, microjets are propelled by bubbles and travel at impressively fast speeds, up to mm/s.22 They have recently been studied for a number of potential applications including cell sorting and transport.20, 23-25 Magnetically driven motors are another emerging class of micromachines26-31 which, like flagellar bacteria, convert body rotation into axial translation.26, 28, 29 Although these motors are in general not autonomous, the external field provides precise control over their movement.

While much effort has been devoted to increasing the speed and functionality of catalytic motors, few papers have commented on the efficiency with which they convert the free energy stored in fuel to mechanical energy. A power conversion efficiency on the order of 10-9 was estimated by Paxton et al. for Au-Pt nanorod motors in hydrogen peroxide solutions.32 A light-to-

mechanical energy conversion efficiency on the order of 10-14 can be estimated for self- thermophoretic micromotors reported by Sano and coworkers based on the laser power, the adsorption of thin gold caps and the velocity of the motors.33, 34 Metallic nanomotors with concave ends propelled by MHz ultrasound are found to have efficiency roughly on the order of

10-7.35, 36 In contrast to these low experimental efficiencies, the movement of nanodimers and catalytic nanoparticles has been calculated from molecular dynamics simulations, and a maximum thermodynamic efficiency on the order of 10-4 was found for both systems.37, 38

However, the small size of these hypothetical nanomotors and their operation under idealized conditions (separate dimers with attractive or repulsive inter-dimer potentials and catalytic particles in gaseous fuels, respectively) makes it difficult to compare them with experimentally studied nano/micromotors. Sabass and Seifert found computationally that the efficiency of diffusiophoretic nano/micromotors should increase with decreasing motor size.39, 40 However there are so far no studies that attempt to model and also measure the efficiencies of nano/micromotors (self-electrophoretic, bubble-propelled, or magnetic helix) that have been experimentally fabricated.

The high power conversion efficiency of biological motors confers many advantages, including the ability to run for long periods of time using on-board fuel, and to use oxidants that are present in low concentration or consumed in slow catalytic reactions. For example, aerobic organisms are able to use oxygen in metabolic reactions despite its low concentration (~0.3 mM) in air-saturated water. The efficiency of intracellular motors in biology is typically quite high. For example, kinesin-based microtubule motors are estimated to have a chemical to mechanical energy conversion efficiency in the range of 60%.41 Because synthetic nano/micromotors are many orders of magnitude less efficient, they are usually studied in solutions that contain high concentrations (~1 M) of hydrogen peroxide or other fuels. A broader choice of fuels (including, for example, glucose/oxygen) would be available to catalytic motors and pumps if their efficiency can be increased by 3-4 orders of magnitude or more. Understanding the sources of energy loss

in catalytic motors is thus important to broadening their range of emergent properties and applications.

2.2 Experimental details

2.2.1 Synthesis of nanorods and nanotubes

The synthesis procedure of the nanorods (nanomotor) was adopted and modified from previous work in our group42-45. Anodic alumina membranes (AAO, purchased from Whatman

Inc., 200 nm pore size) were used as the template for the electrodeposition of metals. The metal plating solutions were purchased from Technic Inc. and were used as received. 5 nm of Cr and

350 nm of Ag were evaporated by using a Kurt Lesker Lab-18 electron beam evaporator on the back side of the AAO membrane (branched side) to serve as the working electrode. A Pt coil was used as the counter electrode. For the deposition of Ag, Au or Pt, a two electrode system was generally used with the Pt coil serving as the pseudo-reference electrode. In this case, current was controlled to be constant. For the deposition of Ru, a three electrode system with Ag/AgCl in 3M

NaCl as the reference electrode was used, and rods were grown at constant potential. In a typical deposition procedure, a ~ 10 µm silver segment was first deposited into the AAO membrane as the sacrificial layer. Then segments of metals (or polymer) of interest were grown. The lengths of the segments were controlled by monitoring the charge passed. The plating conditions for Ag, Au, and Pt were -1.77 mA/cm2, -1.24 mA/cm2 and -1.77 mA/cm2, respectively. Ru was deposited at a constant potential of -0.65 V vs Ag/AgCl. Multi-segment nanorods were synthesized by replacing the plating solution without disassembling the plating cell, with a rinsing step in between. After the electrodeposition step the membrane was thoroughly rinsed with DI water and dried, and usually one half of membrane was soaked sequentially in 1:1 v/v HNO3 and 0.5 M NaOH to dissolve the silver and the alumina membrane, respectively. After that the wires were sonicated

and washed in DI water several times until the pH was neutral (centrifuge is used in between each rinsing to sediment the wires to the bottom). Please note that in order to ensure the surface of the nanowires fabricated is clean, all the soaking and cleaning steps must be carried out in clean glass wares to avoid contamination. Glass Pasteur pipets instead of plastic pipets need to be used. An easy way to identify whether the wires are clean during the cleaning steps is to check if the wire aggregate at the bottom of the container (glass test tube) after each centrifuge step starts to “climb” up the container wall. Clean wires would appear to be climbing up the test tube side wall. The number of nanowires is roughly 2×109 per one whole AAO membrane.

The AuRu nanotube was fabricated by first evaporating a layer of gold on the back of

Whatman AAO 200 nm membrane. Then polyaniline was electrodeposited into the pores of the membrane by sweeping the voltage from -0.2 V to 1.2 V vs Ag/AgCl reference electrode for 50 cycles. This produced an array of polyaniline nanorods of roughly 10 μm in length that appeared dark colored under the optical microscope. After the deposition of polyaniline the membrane was dried by nitrogen and then soaked in 1M NaOH for 4 min to slightly etch the side walls of the

AAO pores. After being thoroughly rinsed immediately following the NaOH etching, the membrane was put into oven at 80 °C for overnight. At this temperature the water evaporates from the polyaniline and the wires shrink slightly. Together with the etching of the side wall, this created a small gap between the polyaniline nanorods and the pore, thus enabling the deposition of metal nanotubes. Metals of interest were then sequentially deposited into the gap following the regular deposition procedures. Polyaniline was removed with concentrated HNO3 after the deposition of metals. The metal nanotubes were then released from the membrane and rinsed clean. If polypyrrole is desired, it can be electrodeposited at +0.7 V vs Ag/AgCl. Note that at the potential to deposit polypyrrole, silver is oxidized and dissolved, and therefore in this case a short gold plug was plated in the membrane instead of silver sacrificial layer. Also gold is evaporated on the back of the membrane to serve as the electrical contact instead of silver. Gold can be removed by commercial gold etchant or iodine/iodide solutions.

2.2.2 Motor tracking

A detailed procedure for tracking of the motor motion can be found in our previous

42 work. In general bimetallic nanorods were suspended in 5% H2O2 solution for at least 15 min before taken for observation. An Olympus BX60M optical microscope (reflective mode) and a commercial video capturing bundle (Dazzle video creator plus) were used for observing the particles and recording videos, and typically an overall magnification of 500× or 1000× was used to take a video clip of 30 s at 30 frames per second. Dark field is especially ideal for observing the motion of nanorods due to the reflective nature of the metal material. For most of cases, the observation cell was simply a piece of rectangle capillary tube (VitroTubeTM from VitroCom,

0.2×2.00 mm, Catalog # 3520-050), which was filled with nanorod suspension by capillary effect.

The video was then loaded with PhysMo 2, an open source tracking software (PhysMo -

Video Motion Analysis Package, http://physmo.sf.net), and the coordinates of the metal rods as a function of time were recorded. Further data analysis was done in Microsoft Excel 2010. Rod speed was calculated by dividing the displacement of the rod center between two frames by the time interval (0.033 s), then taking the average of the speed over the selected tracking period.

Errors were introduced to the tracking data by the manual process involved in obtaining the coordinates of the moving nanorods. However the tracking was repeated with multiple rods (at least 10 data points for each rod) to ensure statistically robust results.

In the experiments where the wall effect is examined more closely, a different observation cell setup was used. In this setup one ring shaped double sided tape was attached on a piece of glass slide (PEG coated or regular). 50 μL of nanorod suspension was added to the center of the tape, followed by placing a piece of glass cover slip on the top to seal the cell. The regular glass slide was pre-cleaned in Piranha solution (concentrated H2SO4: 30% H2O2 =3:1. Caution!

Extremely corrosive! Proper PPE and care needed when handling Piranha solutions!) Au-Pt nanomotors moved at an average speed of 9 ± 2 μm/s and 14 ± 3 μm/s in cells made of a regular

glass slide and a PEG coated glass slide, respectively. The relatively small zeta potential of PEG coated glass slide gave the nanomotor a ~60 % speed increase. The significant difference in the nanomotor speeds between in a capillary tube (21 ± 5 μm/s, tube is also made of regular glass) and a cell made of a regular glass slide (9 ± 2 μm/s) is most likely due to the introduction of impurities by the use of adhesive in the construction of the observation cell. It has been previously reported that the activity of electrophoretically driven bimetallic nanomotors is very sensitive to even a very small amount of salt in the solution. Therefore it is only appropriate to compare nanomotor speeds in cells constructed in the same way, while capillary tubes lead to higher nanomotor speeds due to the pristine inner surface of the tube that is in contact with the nanomotor suspensions. Please note that capillary tubes are used exclusively in our experiments as the observation cell except for the experiments in which the wall effect is studied. This is because the inside of the capillary tubes are well protected from contamination.

2.2.3 Oxygen evolution experiment

Nanorods of interest and of known concentration were mixed with 5% H2O2 aqueous solution for at least 15 min before the experiment. The suspension was then transferred to a 10 ml test tube, which was then sealed tight and purged with Ar gas before sampling. For each sampling,

500 μL of Ar was injected into the test tube followed by taking 500 μL of the air sample from the tube and injecting it into GC machine. The oxygen evolution rate per wire was calculated after carefully taking into account of the oxygen from the air leaked in, the volume of the gas in the test tube and number density of the wire in the suspension. A control experiment with 5% H2O2 in the absence of catalytic nanorods was carried out for comparison, with all the other experiential parameters the same.

2.3 Self-Electrophoretic Catalytic Motors

2.3.1 Calculating the overall energy efficiency

While a number of mechanisms have been proposed to contribute to the propulsion of bimetallic motors in H2O2 solutions, there is good evidence that self-electrophoresis (Fig. 2-1) is dominant for motors in the size range of a few microns and below.11, 42 In this mechanism the oxidation and reduction of H2O2 occur preferentially at the anode (Pt) and cathode (Au), respectively. This results in an asymmetric distribution of protons near the ends of the rod, which in turn creates an electric field outside the metal. Because the metal surface is negatively charged, the rod moves in this self-generated electric field. It is worth noting that a significant portion of the cathodic current is contributed by the reduction of oxygen to water at the gold surface (Eqn.2-

3).42 However this does not affect the mechanism or the product distribution in the overall reaction (Eqn.2-4).

2 2 2 2 2

2 2 2 2 2 2

2 2 2

2 2 2 2 2

The power conversion efficiency of the nanomotor is defined by (2-5),

where and are further defined as,

( )

Here μ is the dynamic viscosity of water, L is the length of the cylindrical rod (3 μm), R

is its radius (150 nm), υ is the motor speed, is the oxygen evolution rate in units of mol/(rod·s)

and is the Gibbs free energy of the decomposition of H2O2 into water and oxygen (Eqn.2-4, -

206.08 kJ per mole of O2 produced). From the O2 evolution rate of Au-Pt nanorods in 5% H2O2

-15 (Fig.2-2, left column), we obtained = 2.3×10 mol O2/(rod·s), and an overall H2O2 consumption rate of 2×2.3×10-15 = 4.6×10-15 mol/(rod·s). We note that this result is slightly higher than, yet on the same order as the results from two previous experiments.3, 42

Figure 2-2. Gas chromatographic measurements of O2 evolution rates from bimetallic motors:

Au-Pt nanorods (left), Au-Ru nanorods (middle), and Au-Ru nanotubes (right). Error bars represent standard deviations from triplicate measurements.

From the oxygen evolution rates (Fig. 2-2) and motor tracking data that gave average axial velocities, the efficiencies of bimetallic rod- and tube-shaped nanomotors could be calculated from Eqns. (2-6) and (2-7). The speed of the Au-Pt nanomotors was 21 ± 4 μm/s, yielding an overall efficiency (sometimes referred to as a thermodynamic efficiency) of 7×10-9, in rough agreement with previous report of Paxton et al. 32 The fastest moving self-electrophoretic nanomotors reported so far have a speed of ~ 150 μm/s, with an Ag-Au alloy as the cathode.6 If these motors consumed fuel at the same rate as Au-Pt nanorods, their energy efficiency would be

-7 on the order of 10 . We note that in calculating the efficiency, the mechanical work refers to the useful work done by the motors.

2.3.2 Energy loss through fuel decomposition

The first stage of energy loss in bimetallic motors comes from the chemical (or non-

46 electrochemical) decomposition of H2O2, which is catalyzed efficiently by Pt. The fuel utilization efficiency of these motors can be expressed as:

The electrochemical decomposition rate was measured by Paxton et al. using Pt-Au interdigitated microelectrodes in H2O2 solutions of various concentrations, and a current density

2 11 of 0.68 A/m was found for 6% H2O2 . Although the geometry of this experiment is different from that of the Au-Pt nanorod, the microelectrode current density provides a rough estimate of the electron transfer rate (and proton flux) at the nanomotor surface. Using this value we obtain

-6 2 7×10 mol/(m ·s) for these fluxes, and the electrochemical H2O2 decomposition rate can be calculated as 0.5-1.1×10-17 mol/(rod·s), depending on the balance of reactions (2-2) and (2-3) at

-15 the cathode. From the total decomposition rate of H2O2 (4.6×10 mol/(rod·s)) we then obtain

-3 -3 = 1.110 to 2.310 . Because Wang et al. found that (2-3) is the dominant cathode

-3 reaction, we estimate to be approximately 1×10 for Au-Pt nanorod motors.

It is apparent from this calculation that the efficiency of nanorod motors could be

3 increased by a factor of ~10 by using metals that selectively catalyze H2O2 oxidation and reduction without catalyzing the overall decomposition reaction. Substitution of Ru for Pt lowers the rate of O2 evolution by 80% (Fig. 2) and the Au-Ru nanomotors move at similar speed (18 ± 3

μm/s) to Au-Pt, resulting in a fourfold increase in efficiency. However Ru is still very catalytically active and decomposes roughly 99% of the fuel chemically, rather than electrochemically. A recent report by Liu et al. described self-electrophoretic Cu-Pt nanomotors

47 operating in dilute Br2 or I2 solutions. Based on the data presented in ref. 47, we calculated an energy efficiency of such nanomotors on the order of 10-5 ~ 10-6, roughly three orders of

magnitude higher than Au-Pt nanomotors operating with the same mechanism. Because the spontaneous chemical decomposition of B2 or I2 on the nanomotor surface is not significant, the

-3 higher energy efficiency of the Cu-Pt motors are consistent with our discussion ( ~ 10 ) and therefore enables the motors to move at speeds up to 20 μm/s in solutions of much lower concentrations (2 mM halogen).

2.3.3 Energy loss from inefficient electrochemical reactions

A second stage of energy loss arises from the use of a very exoergic reaction to generate a small potential drop along the surface of the nanomotor. The electrochemical potential of the cell (Eqn.2-4) can be calculated as 1.07 V from Eqn. 2-9:

The potential difference (Δϕ) in the solution between the two ends of a Au-Pt nanomotor, at a surface proton flux of 7×10-6, was found by finite difference simulations to be 2.1 mV. An efficiency term, tentatively termed cell efficiency, is defined to account for this loss of energy,

-3 For the Au-Pt catalytic nanomotors, is calculated to be ~2×10 , again on the order of 10-3. It is interesting to contrast this value with the near-unit efficiency of biological motors that are driven by proton gradients, such as ATP synthetase. The biological motors operate near the reversible limit through a tight coupling of mechanical work to the movement of protons along a pH gradient. In the present case, the proton gradient and resulting electric field established by the reaction is depolarized by convection, electromigration and especially by rapid diffusion of protons from the anode to the cathode.

Referring to Fig. 2-1, oxidation and reduction occur preferentially at the Pt and Au ends of the nanorod, respectively. Protons are generated at the Pt end and consumed at the Au end,

leading to a concentration gradient of protons around the rod (see Fig. 5-4 for the numerically simulated proton concentration profile). The proton concentration gradient drives them by diffusion from the anode to the cathode. In addition, the protons are subject to migration in the same direction in the self-generated electric field, and convection in the frame of the moving rod.

The transport of ions is governed by the general flux equation (Eqn. 2-11),

where Ji is the flux of ion i and the three terms on the right represent convection, diffusion, and migration, respectively. Far from the surface of the motor, the flux and each of the gradient terms are zero, but at the motor surface JH+ is related to the current density j by JH+ = Fj.

Here u is the fluid velocity, ϕ is the electrostatic potential, R is the gas constant, F is the Faraday constant, T is the absolute temperature and ci, Di, zi are the concentration, diffusion coefficient and charge of species i, respectively.

The respective contributions of diffusion, electromigration and convection to the transport of protons can be estimated by numerical simulation (Fig. 2-3, see Chapter 5 for simulation details). For protons moving along the long axis of the nanorod, electromigration is dominant, contributing ~68% of the overall flux. The diffusive flux is ~29% and convection is relatively unimportant at ~3% (Fig. 2-3b). On the other hand, for proton transport away and towards the nanorod (perpendicular to the direction of motion), diffusion accounts for nearly 99% of the overall flux (Fig. 2-3c), while proton transport by electromigration and convection are negligible.

Figure 2-3. Numerical simulation to determine the contributions of diffusion, electromigration, and convection to proton transport. (a): Steady-state proton distribution around a Pt (top)-Au

(bottom) catalytic nanomotor (3 μm long and 300 nm in diameter) with a surface flux of 7×10-6 mol/(m2∙s). Red and blue represent high and low proton concentration (units in legend: mol/m3).

Arrows illustrate proton flux contributions (arrow lengths are not in exact proportion to the flux);

(b): Proton fluxes from diffusion, electromigration and convection along the nanorod long axis across the center line (dashed line in (a)); (c): Proton fluxes perpendicular to the nanorod surface from the top half (Pt end, across the black line in (a)). In (b) and (c) fluxes were integrated over the respective cross-sections.

This simulation shows that the diffusion and electromigration fluxes, which are both proportional to DH+, the diffusion coefficient of protons (Eqn. 2-11), are together responsible for the dissipation of the proton gradient generated by the electrochemical reaction at the Pt-Au

-5 2 o 48 nanorod surface. Thus the value of DH+ , which is 9.3×10 cm /s in pure water at 25 C, can affect the speed and efficiency of the motor. By varying the diffusion coefficient of protons in the model, the calculated motor speed could be varied by a factor of three or more, as shown in

Fig. 2-4. Posner et al. found that the speed of self-electrophoretically driven motors is inversely

proportional to the proton diffusion coefficient in their scaling analysis of the Au-Pt nanomotor system.49 Although the result obtained by numerical modeling in Fig.2-4 is not strictly inversely proportional, it shows a similar trend.

Experimentally it is difficult to manipulate the proton diffusion coefficient without significantly altering other parameters of the system, such as viscosity or temperature. However, it is possible to limit proton diffusion by spatial confinement. In order to test this hypothesis, we fabricated bimetallic nanotubes in which both the inner and outer surfaces were catalytically active. These tubular nanomotors, as a result, should generate a higher proton flux and also inhibit

diffusion of protons out of the tube to significantly increase the electric field and consequently the motor speed.

Numerical modeling of these tubular nanomotors shows that they indeed trap protons inside the tube and increase the local proton concentration significantly (Fig. 5-11). We fabricated

Au-Ru nanotubes by a modification of the template-assisted electrodeposition process described by Shin et al.50 Fig. 2-5 shows field emission SEM images and a cartoon of the structure of these nanotubes.

Figure 2-5. FESEM images of Au-Ru nanotubes. (a) side and (b) end-on view.

The Au-Ru nanotubes moved at a speed of 32 ± 5 μm/s in 5 % 2O2 solution, roughly 75% faster than solid Au-Ru nanorods of similar dimensions (18 ± 3 μm/s). The nanotubes move with their Au end leading, and no bubbles were observed, which is consistent with the self- electrophoretic mechanism. Gas chromatography experiments showed that the rates of O2 evolution for nanotubes and nanorods were statistically the same, with differences within experimental errors. Because the drag force scales as v2 (Eqn. 2-6), the efficiency of the tubular

Au-Ru motor is higher than that of cylindrical Au-Ru and Au-Pt motors by factors of 3 and 12, respectively.

The fact that oxygen was not produced at a significantly faster rate from the AuRu nanotubes than the AuRu nanorods suggests that the mass transfer of H2O2 into the tube is limited

by the geometry. As a result, the decomposition of H2O2 on the inner surface is slower and it produces a lower flux of protons than on the outside of the tube. Nevertheless, simulations show that even if the flux on the inner surface is only 10% of that on the outer surface, a significantly higher proton concentration develops inside the tube (see Fig. 5-11).

2.3.4 Energy loss through inefficient propulsion mechanism

The third stage of energy loss concerns the fraction of electrical energy, represented as the potential difference between the anode and cathode ( ), that is converted into mechanical work. The nanomotor equivalent circuit can be represented as a DC voltage source in series with the solution resistance, as illustrated in Fig.2-6.

For this stage we can define a propulsion efficiency by Eqn. 2-12:

-18 where is the mechanical power of the nanomotor (calculated to be 3.3×10

W/rod), is the electrical power that is generated by the calculated 2.1 mV potential

difference , and I is the current flowing in the system. Taking the current density to be 0.68

A/m2 and the surface area of each end of the rod as 1.48×10-12 m2, a current of 1.01 pA is

-15 -3 -3 calculated. Therefore Pelec is 2.1×10 W/rod, and ηprop is 1.6×10 , or on the order of 10 . This component of the overall motor efficiency is sometimes referred to as the hydrodynamic efficiency.

The inherently low efficiency of this stage can be understood in terms of the electrophoretic force acting on a charged particle. This is most simply modeled for a Janus sphere of radius r, for which the electrophoretic velocity v is:

Here  is the zeta potential of the particles, which Paxton et al. measured as -40 mV for

Au rods in deionized water.11 The electric field E can be approximated as the potential drop

divided by the path length l around the sphere, πr. The other terms in the equation are , the

-12 relative permittivity of water (80.1), the vacuum permittivity (8.910 F/m), and , the viscosity of water (110-3 Ns/m). The drag force on the sphere is given by the Stokes law, and the mechanical power can be calculated as the product of the drag force and the velocity:

The electrical power can be calculated as the current-voltage product, i.e.,

where j is the current density and the area of one half of the Janus particle is 2πr2.

Combining these terms we obtain the efficiency as:

( )

The last term in this equation can be simplified by expressing Δ j in terms of the resistivity  of the solution, which Paxton et al. measured as 2.5103 m for suspensions of gold nanorods in water,

( )

Combining these equations we obtain:

-3 and substituting the values given above with r = 1 µm, we calculate prop ≈ 2  10 , in reasonable agreement with the measured value. This result shows that electrophoretic energy transduction should be inherently inefficient with motors in the micron (and larger) size regimes,

2 especially in electrolyte solutions with low (e.g., high ionic strength). The 1/r scaling of prop suggests that sub-micron swimmers might have higher efficiency.

2.3.5 Energy loss through opposite electro-osmotic flow near the charged substrate

The fourth stage of energy loss for bimetallic catalytic motors is the electroosmotic flow of fluid at the bottom of the glass cell, which opposes the direction of electrophoretic propulsion for negatively charged nanorods. Because the nanorods are made of dense metals, they sink to an equilibrium position slightly above the bottom wall of the cell. Their height above this glass surface is determined by a balance of the downward gravitational force and the electrostatic repulsion between the rod and the glass. The electroosmotic counter-flow is illustrated in Fig. 2-7.

Because of the close proximity of the nanomotor to the wall (500 nm to 1 μm), the effect of electroosmotic flow can be significant. In fact, there are cases where local electroosmotic flow dominates over the electrophoretic transport of particles and causes them to move in the opposite direction.11, 51, 52 To further confirm the existence of the reverse electroosmotic flow and estimate its effect on the motors, we compared the movement of Au-Pt nanomotors suspended in 5% H2O2 over an uncoated glass slide and one coated with poly(ethylene) glycol (PEG). The PEG coating imparts a smaller (~-10 mV) charge to the surface.53-55 Nanomotors moved ~ 60% faster over this surface than they did over uncoated glass slides, which typically have zeta potentials of -60~-90 mV. 56 Taking into account that the mechanical power of the nanomotor scales as the square of its velocity (Eqn.2-6), we can define an efficiency related to this wall effect:

( )

where υ is the observed velocity of nanomotors with the wall effect, and the velocity of motors in its absence of the effect. Based on the difference in the speeds for nanomotors moving near walls of different zeta potentials, we can estimate .

This effect can be minimized by lowering the charge density of wall, as illustrated in the

PEG experiment. However, the nanorods are maintained above the wall by electrostatic propulsion, and they adhere to walls of opposite charge. Thus a more thorough analysis is needed to evaluate the optimal surface charge on the bottom wall that gives the highest efficiency. An alternative is to increase the negative surface charge on the nanomotor, which should increase its speed and, through electrostatic repulsion, its distance from the bottom wall.

The energy loss due to the wall effect is on the order of 10-1, which is less significant than the other three energy loss pathways, each of which have values of about 10-3. The wall effect can however be important for large and/or dense micromotors. In such cases the distance between the motor and the wall is small compared to the size of the motor. In the presence of a large cargo, depending on its dimensions and density, the wall effect could generate stronger backward electroosmotic flow or hydrodynamic drag that significantly slows down the motor.

2.4 Catalytic Bubble Motors

It is interesting to compare the efficiency of self-electrophoretic motors with those that utilize other propulsion mechanisms. In two cases, the propulsion efficiencies are relatively straightforward to estimate: micromotors driven by bubble propulsion14, 17, 18, 57 and magnetically driven helical micromotors.26, 28, 29 These two types of motors have been well studied and are being investigated for a variety of applications, including those in biological environments.20, 22, 24,

25, 58

Tubular catalytic micromotors, first reported by Solovev et al.,14 are propelled by oxygen bubbles generated in the decomposition of H2O2. Motors of different dimensions and bubble production rates result in different velocities. For example, multi-layered 5.5 µm diameter

14 microtubes 100 μm in length were reported to jet through 3% 2O2 solution at 50 μm/s. In 3%

H2O2, the microtubes generate 34 μm radius bubbles at a rate of 1.5 per second. Using the ideal

gas law, the oxygen evolution rate is 1.10×10-11 mol/(tube·s), corresponding to a chemical input power of 2.27×10-6 W/tube. The mechanical power output can be calculated from the velocity

(Eqn. 2-6), to be 5.46×10-16 W/tube. The ratio gives an efficiency of 2.40×10-10, which is comparable to that of self-electrophoretic nanomotors. A similar analysis applied to bubble- powered Janus sphere micromotors59 gives a calculated efficiency of 5×10-10.

The low efficiency of bubble-powered micromotors can be understood qualitatively in terms of two stages of energy loss. The expansion of the oxygen gas into bubbles large enough to detach from the particle surface is a prerequisite to motion. The expansion power of the oxygen bubbles can be estimated, assuming the ideal gas law and reversible expansion, to be 2.50×10-8

W/jet. Thus the work of bubble expansion constitutes ~1% of the chemical input energy, and 99% of the energy of the reaction is simply dissipated as heat. The second stage of energy loss derives from the fact that at low Reynolds number, propulsion happens only at the instant of bubble release. Careful examination of microtube motion has shown that the motors are stationary except for sharp spikes of movement corresponding to bubble release.19 At low Reynolds number (10-4 -

10-5), the timescale of acceleration and deceleration is on the order of microseconds, and the recoil movement persists only over this short time period. Further, because the momentum of the bubble and motor must be equal and opposite at the instant of release, some of the kinetic energy goes into the bubble and the viscous layer of water between its surface and the shear plane. The combination of these effects apparently results in a second-stage efficiency of ~10-8 for bubble motors, making their overall efficiency ~10-10.

2.5 Helical Micromotors

It is also interesting to consider the efficiency of helical micromotors, which so far have been powered with external magnetic fields. This class of micromotors is especially interesting because of their resemblance to flagella bacteria, which combine their helical form with catalytic

propulsion. In an externally applied rotating magnetic field, helices of ferromagnetic materials respond to the field and rotate. The torque translates into an axial force, which results in directional motion of the micromotors. The torque, axial force, linear velocity and angular velocity of the motor can be related via a 2×2 Purcell matrix60

[ ] [ ] [ ]

where F is the axial force (which equals the drag force on the micromotor at low

Reynolds number), N is the torque (in N·m), υ is the velocity of the motor and Ω is the angular velocity (in rad/s). This matrix gives the efficiency, :

This calculation does not take into account the magnetic energy absorbed by the medium surrounding the motor, or the heat generated in the electrical circuit that controls the magnet. It accounts only for the mechanical energy imparted by magnetic induction and the fraction of that energy that is converted to axial movement. Thus,  represents an upper limit for the efficiency of the motor.

Among several reports on helical micromotors, one by Nelson et al. provides details about the Purcell matrix, axial force and torque.26 For a 38 μm micromotor in a 2 mT magnetic field, the Purcell matrix was found to be:

[ ] [ ]

As a result the maximum drag force, torque, angular velocity and motor velocity were derived as 3.0×10-12 N, 4.3×10-17 N·m, 190 rad/s and 1.8×10-5 m/s, respectively. These values give  = 0.66%, i.e., on the order of 10-2~10-3. This is slightly higher than the hydrodynamic propulsion efficiency of electrophoretically driven (10-3) or diffusiophoretically driven (10-3)39, 40 motors in the micron size range.

The hydrodynamic efficiency of these helical motors is comparable to that of flagellar bacteria. Purcell calculated that the maximum efficiency of rotating flagella is ~1%.61 The experimental efficiency of E. coli propulsion has been estimated to be around 2%.62, 63 Purcell has pointed out that the energy consumption of a flagella bacterium is negligible compared to its energy intake in an environment where nutrition is abundant. Propulsion mechanisms of low energy efficiency are therefore biologically viable in such cases.

2.6 Conclusions

In conclusion, we find that both self-electrophoretic and bubble-powered catalytic micromotors have efficiencies, defined as the fraction of chemical input energy that is converted to mechanical work, on the order of 10-9-10-10. These low efficiencies can be understood in semi- quantitative terms as sequential stages of energy loss. We note that a broader range of functionality could be available to catalytic micromotors if their efficiency could be increased by

3-4 orders of magnitude, including operation using dissolved O2 as the oxidant. The simplest path to increasing the efficiency of self-electrophoretic motors is to eliminate the background catalytic consumption of fuel, and this idea has already been demonstrated with bimetallic copper-halogen micromotors. It is interesting to note that helical magnetic micromotors have 6-7 orders of magnitude higher efficiency, and this suggests that a key challenge in the field is to learn to power such motors chemically.

2.7 References

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Chapter 3 Dynamic motor interactions and particle assembly driven by catalysis on the surface of bimetallic nanorods

3.1 Introduction

Dynamic interactions between moving objects, in particular how they respond to external stimuli and communicate with each other, have long been studied and still remain one of the most interesting topics for scientists. Schooling of fish and flocking of birds are good examples of the interactions between macroscale objects moving in orchestrated and constant communication. In these systems, macroscale organization is typically driven by nearest-neighbor interactions that follow simple rules. To reach this level of complexity however, fast and precise (in terms of distances, angles, and velocities) communication and response are required from the members.

Despite the intense effort and substantial progress in the field of artificial intelligence, dynamic collective behaviors as complicated as fish schooling have not been demonstrated in macroscopic synthetic systems. On the other hand, self-assembly at the nano- and molecular levels demonstrates a certain level of complexity and has furthered our understanding of organization and assembly at small scales.1, 2

A great many examples of particle interactions at micrometer or larger scales have been demonstrated. External fields such as light, magnetic, electric and acoustic fields have been commonly exploited to manipulate inactive particles.3-6 Janus colloidal particles can also self- assemble through various mechanisms.7-11 However in these examples the assembly of particles hardly approaches the complexity level demonstrated in living organisms; these interactions are passive responses to external fields with very limited inter-particle communication or inter- particle interactions.

Interactions between active particles, on the other hand, become much more interesting as they can result in collective and emergent behaviors. Such active microparticles generate signals typically in the forms of gradients of chemical concentrations, pressures or electric potential.

Such gradients can induce responses from nearby particles, and when the particle number density is high collective behaviors can emerge. For example, rotating millimeter scale objects were found to undergo dynamic aggregation and assembly and as a result, formed organized patterns.12,

13 Recently the interactions between autonomously moving nano- and micromotors and the collective behaviors they demonstrate have also attracted a significant amount of interest.14 Such collective behaviors as a result of a chemical gradient include swarming and schooling,15-19 predator-prey interactions,18 dynamic attraction and repulsion between rotors,20, 21 spatiotemporal oscillations15, 22,15, 22 and self-assembly. 21, 23 Hydrophobicity and hydrodynamic interactions can also drive the organized assembly of nanomotors.24, 25 Theories and simulations have furthered the our understanding of the interactions observed in these systems.24-28

Here we report dynamic motor-motor interactions and particle self assembly caused by self-electrophoretically driven bimetallic nanomotors. These nanomotors, first reported in 2004, are made of bimetallic nanorods and when placed in diluted H2O2 can move autonomously at a speed of ~ 20 μm/s.29-31 We have observed that such active nanomotors can actively associate with nearby motors and form rotating doublets of staggered shapes or linearly moving triplets in a dynamic process. In addition, when the nanomotor is mixed with charged tracer particles, it acts as a microtransporter that carries and assembles cargos. This is the first observation of such phenomena in systems of bimetallic rod motors and as such is an interesting addition to the study of dynamic interactions of nanomotors and colloidal particles in general.

3.2 Interactions between autonomously moving nanomotors

Bimetallic Au-Pt nanorods, when suspended in H2O2 solution (typically 5 wt%), show autonomous motion at axial speeds in the range of 10 body lengths/second. There is good evidence that this motion is primarly driven by a self-electrophoretic mechanism 30, 32, 33.32, 34, 35 In suspensions of H2O2, H2O2 molecules are oxidized and both H2O2 and O2 are reduced preferentially on the anode (Pt) and cathode (Au) segments of the rods, respectively. This results in an asymmetric distribution of protons and counter anions around the nanomotor. This self- generated electric field drives the movement of negatively charged nanorods in a manner similar to electrophoresis. The proton distribution and electric field, which will be discussed later, play a critical role in the dynamic interactions between these nanomotors, as well as between nanomotors and tracer particles.

3.2.1 Key observations of nanomotor interactions

Several key observations are listed as follows and illustrated in Fig. 3-1. Autonomously moving Au-Pt nanorods bind asymmetrically into doublets of staggered shapes when moving close to each other (Fig. 3-1a). The doublet usually starts to rotate to either side. In addition such doublets are formed almost exclusively by two nanomotors moving in the same directions, while motors moving in the opposite directions quickly move past each other without noticeably interacting (Fig. 3-1b). This kind of interactions were observed only for active nanomotors; inactive nanorods (e.g. rods with only one metal component) were only affected by Brownian motion as well as by long range repulsive electrostatic forces between rods. In addition, the attachment between two moving nanomotors was reversible in that they could separate and resume their individual motion, or recombine after separation. Although not frequently observed,

the doublet could attract a third nanomotor and form a triplet (Fig. 3-1a). The shape of such triplets was less asymmetric and therefore led to a relatively linear trajectory.

3.2.2 Interaction mechanisms

Aggregation of nano- and microscale particles is a common phenomenon, and can usually be attributed to a wide range of attractive forces including van der Waals attraction, electrostatic attraction between opposite charges, capillary forces,34 magnetic attraction if the

particles are magnetized, and induced dipole-dipole attraction in AC electric fields. 3 All these can be excluded except for van der Waals forces and electrochemically generated electrostatic forces, based on the particular system being investigated. To be specific, the van der Waals force becomes strong enough to bind two metallic microrods when they are close to each other.

However it does not explain the staggered shape of the doublet formed by two nanomotors, nor could it be solely responsible for the binding between two nanomotors because bimetallic nanorod suspensions at the absence of H2O2 are stable with minimal aggregation. Therefore there have to be additional forces that exist only when the bimetallic nanorods are exposed to H2O2.

The mechanism we propose to explain the formation of doublets of staggered shapes is based on the electric field generated by the nanomotors and the charged ionic clouds around each end of the motors. First, when two nanomotors move close to each other, their respective electric fields overlap with each other and could result in stronger or weaker electroosmotic flows. Fig. 3-

2 shows simulation results of the electric field strength in the direction along the long axis of the nanomotors (z direction in the 3D simulation). It is clear that when two nanomotors moving in the same direction move close to each other (1 μm separation), the electric field between the two nanomotors is reinforced (Fig. 3-2, red square. The electric field in this case is ~1.8 times stronger than the electric field generated by one nanomotor). If we consider the nanomotor as a stationary pump with negative surface charges, then the electric field along its surface induces electroosmotic pumping of the fluid around it (black arrows in Fig. 3-2). Therefore a stronger electric field between two nanomotors would induce a faster electroosmotic flow in the center.

Although we do not have a quantitative model of the effect of enhanced flow between two moving nanorods, conceptually we can propose a convection loop that returns fluid to the outer surface of the nanorod pair. This should lead to a pressure gradient that pushes the nanorod motors towards the center, which explains the attraction between two nanomotors moving in the same direction. The simulation results also suggest that the electroosmotic flow is weaker

between two nanomotors than it is on the outside when they move in the opposite directions (Fig.

3-2, orange circle). In such a case no binding occurs between the two nanomotors.

The staggered shape of the doublets formed by two nanomotors could originate from surface reactions on the nanomotors. As was briefly mentioned previously, H2O2 is oxidized at the cathode (Pt) and reduced at the anode (Au), as described by the following reaction equations:

2 2 2 (aq) 2(g) 2 3-1

2 2 2 (aq) 2 2 2 (l) (3 2a)

+ - O2 (g) + 4H (aq) + 4e  2H2O (aq) (3-2b)

2 2 2 2 2 (l) 2(g) (3 3)

Therefore protons are produced in excess at the Pt end of a Au-Pt nanomotor, creating more positive charges around this end. Similarly negative charges are generated around the Au end. Naturally this leads to electrostatic interactions between the charged ionic clouds when two nanomotors approach each other. The specific interaction pattern depends on the relative positions of the two nanomotors, as is illustrated in Fig. 3-1. Numerical simulation of the space charge distribution around a Au-Pt nanomotor in H2O2 solution (Fig. 3-3) qualitatively shows that the electrostatic interaction would favor a configuration in which the opposite ends of two nanomotors meet (Fig. 3-3, left), in which case the electrical energy is minimized. Although the simulation results also suggest that two nanomotors moving in the opposite direction can minimize the electrical energy by overlapping in parallel (Fig. 3-3, right), such a doublet is highly unstable and would have only a transient existence, because the shear stress between two nanomotors at high relative speed (~ 40 μm/s) would quickly separate them. We have also observed that faster nanomotors have stronger interactions. This is consistent with the mechanism we propose here because faster nanomotors typically have higher surface reaction fluxes and

therefore higher charge density and stronger electric fields, which leads to stronger attraction.

Figure 3-3. Numerical simulation of the electrostatic interactions between two nanomotors at different relative positions. The coordinates on both x and y axes in the images are indicated in

μm. These images are slices of the xz planes of 3D simulation results. Colors in the images

3 represent the space charge density (ρe in Eqn. 5-2, in units of C/m ), with red being high and blue being low. Artistic renderings of Au-Pt nanomotors are superimposed over the simulation results for illustrative purposes, with Pt being silvery and gold being golden in color. Hollow arrows indicate the directions of the motors’ motion.

3.2.3 Doublet rotation and splitting

Doublets formed by two nanomotors typically rotate towards one side or the other, and eventually split. This is illustrated in Fig. 3-4. The propulsion force of a nanomotor is balanced by the Stokes drag force (Eqn. 2-6), which is linearly proportional to the motor speed. When two nanomotors (motor 1 and 2) at speeds of U1 and U2 (U1 < U2) are moving freely, their propulsion forces are balanced by their respective drag forces. However when these two motors bind into a doublet, they will start to move at the same angular velocity (if rotating). This leads to a speed

’ ’ increase of the slower nanomotor and speed decrease of the faster nanomotor (U1 < U 1, U2 > U 2) and consequently an increase and decrease of the drag force on motor 1 and 2, respectively.

However if we assume the propulsion force is not affected by the binding, then there will be a net force acting on either of the nanomotor, resulting in a net torque that rotates the doublet to the side of the slower motor. This will be further proved by tracking analysis.

Theoretically the doublet can maintain a linear trajectory if the speed of the two nanomotors is the same. This is simply due to the non-uniformity of nanorods grown by electroplating of metals into the pores of anodic alumina membranes. Experimentally there is always a broad distribution of the nanomotor speed, and all the doublets we observed rotate. In addition, Brownian motion constantly affects the relative positions of the two nanomotors in a doublet, and contributes to the splitting of the doublet, as is illustrated in Fig. 3-4b. If the net force of the nanomotor and/or the separation caused by Brownian motion is large enough, the doublet may split, which happens to many of the doublets during the observation window

(seconds to a few minutes).

Figure 3-4. The rotation and splitting of a doublet composed of two Au-Pt nanomotors. Pt is the silver colored segment on the top and gold is at the bottom. (a): Two nanomotors of different speeds (U) undergo speed change when they bind to form a doublet, therefore experiencing changes in drag forces (Fdrag). As a result the non-zero net force (Fnet) acting on either nanomotor creates a net torque that rotates the doublet to the side of the slower motor. Fprop is the propulsion force. (b): The effect of Brownian motion and propulsion force on the doublet. Fatt. is the combined attractive forces that pull nanorods together (van der Waals and pumping effect). kT represents the thermal energy that is responsible for the Brownian motion, and θ is the separation angle between the two nanorods. Depending on the relative magnitude of the propulsion force, drag force, Brownian motion and attractive forces, the doublet can maintain a stable circular path or split.

3.2.4 Tracking analysis of nanomotor interactions

Further insight into the details of the interaction between nanomotors was gained by tracking analysis. Fig. 3-5a show a clear example of the dynamic interaction between two autonomously moving Au-Pt nanorods, whose trajectories are plotted in Fig. 3-5b. In this video two nanomotors attract each other and form a staggered doublet that immediately beings to rotate.

Within one second the doublet disintegrates and the two nanomotors resume their respective trajectories. The speeds of the two nanomotors were Umotor1 = 34 ± 3 μm/s and Umotor2 = 30 ± 9

μm/s before they attached to each other, and dropped to U’motor1 = 30 ± 10 μm/s and U’motor2 = 22 ±

7 μm/s once the doublet is formed.

Tracking results showing the trajectory of the two nanomotors. (c) The relative distance between the centers of the two nanomotors during the period of interaction. Inset in (c) shows the circular trajectory of the centers of the two nanomotors.

When two motors combine to form a rotating doublet, it rotates to the side of the slower motor, as is illustrated in Fig. 3-4a. Fig. 3-5c lends proof to this argument by demonstrating that the doublet rotates to the side of the slower motor (motor 2). In addition, the ratio of the speeds of the two motors when in a doublet (U’motor1:U’motor2=1.4) agrees nicely with the ratio of the radii in which they rotate (determined to be 1.4 from experimental tracking data). This indicates that the two motors, which are constrained to move at the same angular velocity, retain their ratio of axial speeds. Furthermore the distance between the centers of the two nanomotors stabilized at 1.0 ±

0.3 μm once they formed a doublet (1.5 μm in theory), and a clear and linear departure from that value is observed whenever the nanomotors are freely moving. This serves as a quick and accurate way to identify binding and splitting events between nanomotors.

These observations and analysis prove that the strong interaction between two autonomously moving nanomotors is a dynamic and spontaneous process that significantly differs from the individual behaviors of free-moving nanomotors.

3.3 Interactions between nanomotors and charged tracer microparticles

3.3.1 Key observations and interaction mechanisms

In order to confirm that the interaction between two self-electrophoretically driven bimetallic nanomotors is electric in nature, control experiments with charged tracer particles were performed. In these experiments, active bimetallic nanomotors were mixed with non-active microparticles (gold nanorods of similar dimensions to the bimetallic nanorods, unfunctionalized polystyrene (PS) microspheres of 1.67 μm diameter, and gold microspheres of roughly 1 μm

diameter) in 5% H2O2 solution. All three types of tracer particles have negative zeta potential (ζAu rod= -47.4 ± 4.3 mV, ζPS = -64.0 ± 1.9 mV, ζAu sphere= -63.9 ± 7.4 mV). In all three cases the bimetallic nanomotors still exhibited autonomous motion. Charged tracer particles, on the other hand, exhibited typical Brownian motion while not interacting with nanomotors.

Attraction between active nanomotors and charged tracer particles was observed in all cases, yet the attraction between nanomotors and gold nanorods is the weakest and shortest-lived.

This is in contrast to the interaction between pairs of bimetallic nanorods which results in a rotating doublet. The distortion of the trajectory of both the nanomotor and the gold nanorod is usually temporary; the nanomotor quickly cruises past the gold nanorod and they resume their original individual paths. Very rarely do they form doublets, and when they do the doublets split quickly. Such a weak interaction also suggests strongly that the interaction between two nanomotors is not purely due to van der Waals force or electrostatics from surface charges on the rod. Otherwise gold rods would similarly show noticeable interactions with themselves as well as with active nanomotors. Chemical reactions occurring on the motor surface and the resulting electric field therefore play a central role in inducing the interactions.

Gold microspheres (~1μm in diameter), however, exhibited much stronger interactions with active nanomotors. In this case nanomotors readily pick up individual microspheres through a long range interaction. The spheres attach to the nanomotor surface (Pt end), and subsequently more gold microspheres attach until a close packed structure forms at the Pt end of the nanomotor.

The details of these interactions will be discussed later. One reason why gold microspheres appear to be much easier to pick up than gold rods by the nanomotors could be the different viscous drag forces experienced by rods and spheres. Compared to gold spheres of 1 μm diameter moving at the same speed, gold rods (3 μm long and 300 nm in diameter) would experience 30 or

50% higher drag force when they are moving along or perpendicular to their long axis, respectively. Therefore nanomotors carrying a slender gold rod would meet more viscous resistance and more likely disintegrate than those carrying gold spheres.

Polystyrene microspheres when mixed with active Au-Pt nanomotors in H2O2 also showed strong interactions very similar to gold spheres. Because of their uniform size distribution, these PS spheres were chosen for a more in-depth study of the interactions between active motors and charged tracer particles. Fig. 3-6 summarizes the interactions and common types of assembly that were observed.

(positively charged particles). This stacking process can continue until a close packed particle assembly is formed around the moving nanorod.

When moving nanorods approach charged tracer particles (gold or polystyrene microspheres), these particles start to respond to the electric field generated by the moving

nanorod by moving toward it and eventually attaching to its surface. However unlike the case with pairs of nanomotors in which a staggered doublet is formed, spherical tracer particles only stick to one end of the nanomotor. Negatively charged microparticles (gold microspheres or unfunctionalized PS spheres) attach to the Pt end, since the electric field points away from the nanorod at the Pt end, and negatively charged particles migrate up the electric field (Fig. 3-9, inset). The same principle leads to aggregation of positively charged microparticles (1.5 μm amidine-functionalized PS microspheres, ζ= 24 ± 5 mV) on the Au end. Once the particles are fairly close to the nanorod, the van der Waals force begins to dominate and causes the particle to stick. Although the attachment is reversible, as manifested by the detachment of tracer particles from the motor surface through collisions with other particles, it is much more permanent than the attachment between two active motors in a doublet in the sense that motor-sphere aggregates do not spontaneously disintegrate.

The doublet formed by a nanorod and a microsphere has an asymmetric shape, which when combined with the asymmetric distribution of propulsion forces and fluid drag forces, can often lead to rotation, in much the same way as a doublet of nanomotors rotate. However, because the particles being carried by the nanomotor are also exposed to the electric field generated by the motor, they too can respond by electrophoresis and move. This creates a propulsion force acting on the sphere that complicates the force analysis. Depending on the size, position, surface charge and fabrication technique of the spheres and nanorods, the total torque can therefore cause the doublet to rotate either way or in theory even move linearly (very rarely seen). The radius of the circle in which the formed structure rotates is also highly dependent on the above parameters, as well as the assembly of subsequent particles, as will be discussed in the following.

Once the nanorod attracts one particle and forms a doublet, while continuing to move

(mostly rotate), the doublet readily attracts more particles one by one, as illustrated in Fig. 3-6.

Although it is more common for multiple spheres to populate the surface of a metal nanorod, two

(or more) Au-Pt nanorods can share one sphere. In general, particles follow the electric field

gradient and attach to nanorods in a way that maximizes surface population. Such principles naturally lead to a closed-packed assembly of spheres around the nanorod. However microparticles only populate one end of the nanomotor because the electric field around the other end would repel the particles. In addition, only 2D assembly is achieved; no particle is assembled above or below the 2D plane because of the lack of force in the z direction.

3.3.2 Tracking analysis of the migration of PS particles towards nanomotors

Fig. 3-7 presents a good example of how charged tracer particles assemble with free moving Au-Pt nanomotors. In this example one Au-Pt nanomotor interacts with and picks up PS microspheres one by one, eventually forming an aggregate with a nanomotor carrying four spheres in a close-packed pattern. The first three spheres were picked up within three seconds and the tracking data of these three attractive occurrences are plotted in Fig. 3-7.

The attachment of PS microspheres significantly changes the pattern of nanomotor motion. First, the nanomotor trajectory is altered upon the attachment of (especially the first) tracer particles. An Au-Pt nanomotor by itself has a relatively linear trajectory randomized by

Brownian motion (Fig. 3-7, I). When a sphere attaches to the nanorod surface, the trajectory of the doublet typically changes to circular, as is shown in Fig. 3-7, II. Such a shift in trajectory has been discussed above. If the next sphere attaches to the other side of the nanorod (most commonly), the trajectory can be reversed to linear (Fig. 3-7, III). Further addition of spheres on the aggregate causes relatively little distortion of the trajectory, mostly because there is limited asymmetry in the shape of the aggregate (Fig. 3-7, IV).

Second, the speed of the motor is significantly affected by the addition of spheres, as is demonstrated in Fig. 3-8. The general trend is that the speed of the motor-sphere aggregate decreases as more and more spheres attach to the nanomotor. Tracking data from two samples were combined to plot Fig.3-8. Although two samples were used, the similarity of the aggregate speeds with 3 and 4 spheres in these two samples indicates that these two samples are roughly comparable. The assembly of gold microspheres on Au-Pt nanomotors shows a similar trend (data not shown). We note that such a trend qualitatively agrees with a previous report by Solovev et al., who observed that the speed of motor-cargo aggregates decreases with increasing number of cargo particles. 48

Finally, by tracking the speed of the tracer particles during their migration towards the motor, we were able to obtain strong evidence that the attraction originates from the electric field generated by the motors, i.e. through localized electrophoresis. The electric field distribution around the motors was simulated by the COMSOL multi-physics package (see SI for modeling details). Then an electrophoretic speed profile as a function of the distance between the tracer particle and the motor was calculated based on the electric field distribution (Fig. 3-9). This speed profile agreed qualitatively with the tracking data of the first PS particle in Fig. 3-7. Both simulation and tracking results show that the tracer particle is relatively idle at distances more

than a few micrometers away from the motor, and that it accelerates as it moves closer to the nanomotor. Its speed reaches a peak when the PS particle is about 0.5 μm away from the motor, and then drops significantly when it moves closer to the nanomotor. Although they both show a similar trend, the reasons for the speed decrease of PS particle close to the motor are different in the experiments and the simulation. In the simulation, the electric field magnitude tends to zero at the nanomotor surface due to a vanishing potential gradient, resulting in a speed of zero for the

PS particle. However in reality when the PS particle is fairly close to the motor surface, the short range van der Waals force draws it towards the nanomotor, resulting in a non-zero speed.

(normalized to the peak speed). Red data points are from the tracking results of the first PS particle in Fig. 3-7 (and are normalized to the peak speed). The effect of Brownian motion was subtracted from the velocity profile.

The migration of the PS particle towards the Pt end of the nanomotor is a combination of electrophoresis and electroosmosis, dominated by the former. As was discussed in detail in

Chapter 2.3.5, there is an electroosmotic flow near the charged substrate underneath the nanomotor and PS spheres as a result of the electric field generated by the nanomotors.

Electroosmosis would move microparticles, regardless of the surface charge, away from Pt end and towards Au end of a Au-Pt nanomotor. Electrophoresis, on the other hand, would move negatively charged particle towards the Pt end and positively charged particles towards Au end, which agrees with our observations nicely. Therefore the electrophoretic migration is primarily responsible for the migration of PS particles towards the nanomotors. Electroosmosis could, however, slow down the PS particles significantly. This has been observed for nanomotors in

Chapter 2.3.5, and could explain the difference in the speeds predicted by the simulation (peak speed ~ 70 μm/s) and experiments (peak speed ~ 20 μm/s).

3.3.3 Nanomotors as microtransporters

The bimetallic nanomotors transform into microengines once tracer particle aggregates forms, carrying a large number of particles (cargo) in solution at a few μm/s. Over time, more and more of these aggregates form and merge together. Depending on the particular configuration of the merged aggregates, the nanomotors can be asymmetrically distributed along the periphery and provide a non-zero torque to the aggregate, causing it to rotate. Since the power provided by one such nanomotor is very limited, roughly on the order of 10-18 W/rod (Chapter 2), a low rotation rate of only a few rpm could be observed for such large aggregates.

A considerable amount of research effort has been dedicated to designing nano- and micromotors capable of loading, transporting and delivering microscale cargo.35 In particular, various techniques haven been developed to achieve cargo pickup, such as electrostatic attraction,36 specific or non-specific binding,36-40 magnetic interactions,43, 44 hydrodynamic interactions,41 hydrophobic affinity,42 molecular imprinting,43 and even purely mechanical force.47,

48 Most of these cargo transport systems require the cargo and/or the cargo carrier to be functionalized in some way.36-40, 42, 43 Those that do not have such a requirement typically involve the use of magnetic fields to find and manipulate cargo.29, 30, 33, 34 A system that universally applies to generic particles of either surface charge (positive or negative, neutral colloidal particles are extremely rare in water) is therefore a welcome addition. Moreover, the ability to assemble multiple generic cargo particles in an organized way is particularly desirable for complex assembly situations, and is hard to achieve with previously reported systems.48 The microtransporter system we demonstrate here is based on a well-studied bimetallic self- electrophoretic nanomotor system and addressed these challenges positively.

3.4 Conclusions

In conclusion, the dynamic interactions between active bimetallic nanomotors in H2O2 solution were investigated. The formation of doublets of staggered shapes was especially interesting, and was attributed to the combination of long range electrostatic attraction between oppositely charged ionic clouds and short range van der Waals forces. The minimization of electrical energy as well as shear stress drives the formation of staggered doublets of nanomotors moving in the same direction. The non-uniform distribution of propulsion forces in the doublet and as a result non-zero net torque causes the doublet to rotate, and Brownian motion facilitates its disintegration. In addition we have studied the dynamic assembly of charged tracer particles on active nanomotors. Polystyrene as well as gold microspheres can be readily attracted to the

nanomotor ends through electrophoretic forces that originate from the electric field generated by the asymmetric surface reactions on the nanomotor. This is further supported by numerical simulations. The subsequent attachment of non-active tracer particles on nanomotors results in a close-packed assembly, with a decrease in the speed of the assembly. Our study of the dynamic interaction and assembly behavior induced by self-electrophoretic nanomotors potentially informs future designs of intelligent nanomotor systems with complex functionalities.

3.5 References

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15. Hong, Y.; Diaz, M.; Córdova-Figueroa, U. M.; Sen, A., Light-Driven Titanium-Dioxide- Based Reversible Microfireworks and Micromotor/Micropump Systems. Adv. Funct. Mater. 2010, 20 (10), 1568-1576. 16. Kagan, D.; Balasubramanian, S.; Wang, J., Chemically Triggered Swarming of Gold Microparticles. Angew Chem Int Edit 2011, 50 (2), 503-506. 17. Palacci, J.; Sacanna, S.; Steinberg, A. P.; Pine, D. J.; Chaikin, P. M., Living Crystals of Light-Activated Colloidal Surfers. Science 2013. 18. Ibele, M.; Mallouk, T. E.; Sen, A., Schooling Behavior of Light-Powered Autonomous Micromotors in Water. Angewandte Chemie International Edition 2009, 48 (18), 3308-3312. 19. Duan, W.; Liu, R.; Sen, A., Transition between Collective Behaviors of Micromotors in Response to Different Stimuli. J. Am. Chem. Soc. 2013, 135 (4), 1280-1283. 20. Wang, Y.; Fei, S. T.; Byun, Y. M.; Lammert, P. E.; Crespi, V. H.; Sen, A.; Mallouk, T. E., Dynamic Interactions between Fast Microscale Rotors. J. Am. Chem. Soc. 2009, 131 (29), 9926- 9927. 21. Gibbs, J. G.; Zhao, Y., Self-organized multiconstituent catalytic nanomotors. Small 2010, 6 (15), 1656-62. 22. Ibele, M. E.; Lammert, P. E.; Crespi, V. H.; Sen, A., Emergent, Collective Oscillations of Self-Mobile Particles and Patterned Surfaces under Redox Conditions. ACS Nano 2010, 4 (8), 4845-4851. 23. Ebbens, S.; Jones, R. A. L.; Ryan, A. J.; Golestanian, R.; Howse, J. R., Self-assembled autonomous runners and tumblers. Phys Rev E 2010, 82 (1). 24. Lushi, E.; Goldstein, R. E.; Shelley, M. J., Collective chemotactic dynamics in the presence of self-generated fluid flows. Phys Rev E 2012, 86 (4). 25. Thakur, S.; Kapral, R., Self-propelled nanodimer bound state pairs. J. Chem. Phys. 2010, 133 (20). 26. Golestanian, R., Collective Behavior of Thermally Active Colloids. Phys. Rev. Lett. 2012, 108 (3). 27. Thakur, S.; Kapral, R., Collective dynamics of self-propelled sphere-dimer motors. Phys Rev E 2012, 85 (2). 28. Chen, Y.; Shi, Y., Dynamic self assembly of confined active nanoparticles. Chem. Phys. Lett. 2013, 557 (0), 76-79. 29. Paxton, W. F.; Kistler, K. C.; Olmeda, C. C.; Sen, A.; St Angelo, S. K.; Cao, Y.; Mallouk, T. E.; Lammert, P. E.; Crespi, V. H., Catalytic nanomotors: autonomous movement of striped nanorods. J Am Chem Soc 2004, 126 (41), 13424-31. 30. Wang, Y.; Hernandez, R. M.; Bartlett, D. J.; Bingham, J. M.; Kline, T. R.; Sen, A.; Mallouk, T. E., Bipolar electrochemical mechanism for the propulsion of catalytic nanomotors in hydrogen peroxide solutions. Langmuir 2006, 22 (25), 10451-10456. 31. Fournier-Bidoz, S.; Arsenault, A. C.; Manners, I.; Ozin, G. A., Synthetic self-propelled nanorotors. Chem. Commun. 2005, (4), 441-443. 32. Paxton, W. F.; Baker, P. T.; Kline, T. R.; Wang, Y.; Mallouk, T. E.; Sen, A., Catalytically induced electrokinetics for motors and micropumps. J Am Chem Soc 2006, 128 (46), 14881-14888. 33. Moran, J. L.; Posner, J. D., Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis. J. Fluid Mech. 2011, 680, 31-66. 34. Ismagilov, R. F.; Schwartz, A.; Bowden, N.; Whitesides, G. M., Autonomous movement and self-assembly. Angew Chem Int Edit 2002, 41 (4), 652-+. 35. Wang, J., Cargo-towing synthetic nanomachines: Towards active transport in microchip devices. Lab Chip 2012, 12 (11), 1944-1950. 36. Sundararajan, S.; Lammert, P. E.; Zudans, A. W.; Crespi, V. H.; Sen, A., Catalytic Motors for Transport of Colloidal Cargo. Nano Lett 2008, 8 (5), 1271-1276.

37. Simmchen, J.; Baeza, A.; Ruiz, D.; Esplandiu, M. J.; Vallet-Regi, M., Asymmetric Hybrid Silica Nanomotors for Capture and Cargo Transport: Towards a Novel Motion-Based DNA Sensor. Small 2012, 8 (13), 2053-2059. 38. Campuzano, S.; Orozco, J.; Kagan, D.; Guix, M.; Gao, W.; Sattayasamitsathit, S.; Claussen, J. C.; Merkoçi, A.; Wang, J., Bacterial Isolation by Lectin-Modified Microengines. Nano Lett 2011, 12 (1), 396-401. 39. Orozco, J.; Campuzano, S.; Kagan, D.; Zhou, M.; Gao, W.; Wang, J., Dynamic Isolation and Unloading of Target Proteins by Aptamer-Modified Microtransporters. Anal. Chem. 2011, 83 (20), 7962-7969. 40. Guix, M.; Orozco, J.; Garcia, M.; Gao, W.; Sattayasamitsathit, S.; Merkoci, A.; Escarpa, A.; Wang, J., Superhydrophobic Alkanethiol-Coated Microsubmarines for Effective Removal of Oil. Acs Nano 2012, 6 (5), 4445-4451. 41. Gao, W.; Kagan, D.; Pak, O. S.; Clawson, C.; Campuzano, S.; Chuluun-Erdene, E.; Shipton, E.; Fullerton, E. E.; Zhang, L. F.; Lauga, E.; Wang, J., Cargo-Towing Fuel-Free Magnetic Nanoswimmers for Targeted Drug Delivery. Small 2012, 8 (3), 460-467. 42. Gao, W.; Pei, A.; Feng, X.; Hennessy, C.; Wang, J., Organized Self-Assembly of Janus Micromotors with Hydrophobic Hemispheres. J. Am. Chem. Soc. 2013, 135 (3), 998-1001. 43. Orozco, J.; Cortés, A.; Cheng, G.; Sattayasamitsathit, S.; Gao, W.; Feng, X.; Shen, Y.; Wang, J., Molecularly Imprinted Polymer-Based Catalytic Micromotors for Selective Protein Transport. J. Am. Chem. Soc. 2013, ASAP.

Chapter 4 Ultrasonically driven metallic nanomotors

4.1 Introduction

Synthetic micromotors are an emerging class of micromachines.1-3 The micromotors studied so far have been driven by a variety of mechanisms, including electrochemical decomposition of chemical fuels,4-9 magnetic fields,10-15 magnetic interactions between particles,16 electric fields,17, 18 light,19-22 bubble-driven propulsion,23-26 polymerization,27 and diffusiophoresis.21, 28, 29 Micromotors fall into two classes: they can be propelled by external (e.g., electric or magnetic) fields, and therefore move in concert with each other, or they can be propelled by local conversion of energy and move autonomously. Autonomous micromotors display fascinating biomimetic behavior that includes transport of cargo,30-33 chemotaxis,34 swarming, and predator-prey interactions,21, 35 and they have been studied for possible applications in bioanalytical sensing and microfluidics,9, 36-38 However, for motors that can move autonomously, there are issues that limit their practical utility in biological environments. Many catalytic micromotor systems rely on the use of toxic hydrogen peroxide (H2O2) or hydrazine derivatives as the fuel.7-9, 23-26, 30-33 In addition, the high ionic strength of biological fluids is incompatible with propulsion mechanisms based on electrophoresis and diffusiophoresis.5, 8, 10, 11,

17, 24, 26, 29 While external electric and magnetic fields can be used to drive micro-objects in biological media, the resulting motion is not autonomous. Given the current strong interest in microrobotics for medical diagnostics, drug delivery, and minimally invasive surgeries, there continues to be a need for a bio-compatible energy transduction mechanism that can power autonomous micromotors.1, 39, 40

Acoustic energy is an interesting candidate for driving micromotors in fluids, including biological media. Medical applications of sound waves at high frequency, such as

ultrasonography, have been developed for decades and are widely used.41 High frequency sound waves, in particular in the MHz regime, have minimal deleterious effects on biological systems.42,

43 Not only are sound waves in this frequency range safe, they are also a powerful tool for manipulating microparticles. Built upon the experimental discoveries of the acoustic collection of small suspended particles in the early 19th century by Kundt and Lehman,44 and subsequent theoretical work,45-47 the understanding of the ultrasonic standing wave and technological advancements in ultrasonic transducers have made more advanced manipulation of suspended microparticles possible.48-56 For example, suspended microscale spherical particles can be aligned into 1-D lines,49, 50, 55 2-D arrays, and more complicated patterns.48, 52 The 3-D manipulation of microparticles has also been achieved by using the appropriate experimental geometry.56 This kind of positioning, regardless of its dimensionality (1-, 2-, or 3-D) or how the acoustic field is applied (surface acoustic wave or bulk acoustic wave), is usually considered to be the result of collecting microparticles at the nodes of ultrasonic standing waves, and the motion of the particles is driven by a pressure gradient. Acoustic levitation and streaming are also commonly observed during these experiments. They can be attributed to the primary acoustic radiation force and to steady-state fluid flow caused by the variation of the acoustic field, respectively.53, 57 Another interesting aspect of research in this field is the ability to align high aspect ratio particles, such as rods and tubes,58-60 and to rotate particles by using acoustic fields.61,

62 However research in this area has so far been limited and autonomous micro-rod propulsion has not been reported.

In this chapter I describe experiments in which ultrasonic acoustic waves can propel metallic rods in fast (~200 μm/s) axial directional motion as well as in fast in-plane rotation. A self-acoustophoresis mechanism based on the shape asymmetry of the microrods is proposed to explain the ultrasonic propulsion. In addition uptake of gold microrods by HeLa cells after incubation together is observed, and the activity of the gold microrods in ultrasonic standing

waves is largely maintained. On the other hand, simply mixing gold microrods with HeLa cells together results in strong binding between the surfaces of these two particles.

4.2 Experimental details

4.2.1 Acoustic experiments

The acoustic experiment was conducted using a homemade cylindrical cell, as illustrated in Figure 4-1. The cell was made by applying three layers of polyimide Kapton® tape (50 μm thickness per layer), with a circular hole of 5 mm diameter cut in the center, on a piece of stainless steel plate (45 mm × 45 mm × 1 mm). Alternatively a piece of silicon wafer can be used as the chamber substrate. A ceramic transducer PZ26 (Ferroperm, Kvistgard, Denmark) was attached by conductive epoxy glue (Chemtronics ITW, Kennesaw GA, USA) to the back of the metal plate to generate acoustic waves in the thickness mode. The transducer was connected to a function generator that outputted sine waves (5062 Tabor Electronics, Israel), and the signal was amplified if necessary by a dual differential wide band 100 MHz amplifier (9250 Tabor

Electronics, Israel). The signal was visualized with a digital storage oscilloscope (IDS 8064

60MHz ISOTECH, Hanan, Israel).

Figure 4-1. Cylindrical ultrasonic cell. The transducer was mounted on a steel plate at the bottom of the cell. Inset: Illustration of the cell cross-section when the acoustic field is applied.

The particles are shown in the levitation plane. The cell height, h, is defined as the distance between the top cover slip and the bottom wall of the cell.

In a typical experiment, 30 μL of colloidal particle suspension was added to the cell, which was then covered by a square glass cover slip which served as the sound reflector. In the case of metal rods, the suspension normally had a number density of approximately 1×108 mL-1.

Video recording was started at the same time the function generator signal output was turned on.

An Olympus BX60M optical microscope and a commercial video capturing bundle (Dazzle video creator plus) were used for observing the particles and recording videos.

The conditions for forming a standing wave in this cell are described by Eqn. 4-1,

where h is the cell height (acoustic path length) and c is the speed of sound in the medium

(deionized water, c=1492 m/s). The cell was designed to have a height of 180 μm. For the simplest case where n=1, the resonance frequency is calculated from (4-1) to be 4.1 MHz, and at

that frequency a nodal plane forms at the center of the cell where the acoustic pressure is at its minimum (Figure 4-1, inset). Preliminary experiments indicated a resonant frequency of about

3.7 MHz. Therefore sine waves with a frequency of 3.7 MHz and output amplitude of 10 Vp-p (a output power of 23.97 dBm, or 249.5 mW) were typically used as the starting point for experiments, and both parameters were varied continuously.

4.2.2 Pulse mode acoustic experiments

Experiments were also done in pulse mode, where the acoustic power was delivered at the same instantaneous power and frequency, but in trains of pulses. A number of pulses N was delivered over a period of time Tp, where Tp = N/f and f is the frequency. These pulse trains were

63 separated by a repetition time Tr. The duty cycle D is defined by D= Tp / (Tp + Tr). The number of pulses N was varied between 150-800, and the pulse repetition rate (1/ (TP + Tr)) was varied from 1 to 4 kHz. This is illustrated in Figure 4-2.

Figure 4-2. An illustration of the parameters used in the pulsed-mode

4.2.3 Particle synthesis and tracking

470 nm polystyrene microspheres were purchased from Polybead (Cat # 07763, amino functionalized). 2 μm polystyrene microspheres were purchased from Polysciences (Cat # 18327, carboxylate functionalized). Gold microparticles (AuMP, 0.8–1.5 μm, 99.96+ %) were purchased from Alfa Aesar. Nanowires synthesis and particle tracking followed the same procedures described in Chapter 2.

4.2.4 Motor-cell interactions

eLa cells (human cervical carcinoma epithelial cells) were grown in Dulbecco’s modified Eagle medium, (DMEM)-F12 medium (Gibco, CA), with 10% fetal bovine serum

(Atlanta Biologicals, GA), penicillin (100 U/ml), and 100 μg/ml streptomycin (Mediatech, VA) to about 60-70% confluence. After this, cells were trypsinized (Trypsin + 0.05% EDTA, Gibco, CA) and suspended in PBS for acoustic treatment. The PBS buffer solution was made by dissolving 1 bag of commercially available BupHTM phosphate buffered saline pack (Thermo Scientific,

#1890535) in 500 ml DI water. The resulting solution contains 0.1 M phosphate and 0.15 M NaCl, and has a pH value of 7.2.

For a typical experiment that studies the interaction between acoustic motors and HeLa cells in a mixed suspension, gold microrods (~ 3 μm long and 300 nm in diameter) were mixed with live eLa cells (~ 15 μm in diameter when suspended) in PBS buffer solutions immediately after cell culture. For experiments that studies motors behaviors inside HeLa cells, gold microrods were added to the HeLa cell culture medium (~ 10 rods per cells) and then incubated for 6, 24, 48 hrs.

In a typical experiment 30 μL of the suspension of eLa + Au rods (either mixed suspension or incubated suspension) was added to the acoustic chamber and ultrasound of 10 Vp-p

was applied. The frequency was carefully adjusted to the resonance frequency, which varies in each experiment. A different acoustic chamber was used for acoustic experiments involving cells, which has a resonance frequency around 2.4 MHz.

4.3 Results and discussions

4.3.1 Spherical polystyrene particles in ultrasonic standing waves

Experiments were first conducted with polystyrene microspheres (470 nm and 2 μm diameter) to gain an understanding of the motion of spherical particles in the cylindrical acoustic cell. In the absence of ultrasound, colloidal particles suspended in the cell showed ordinary

Brownian motion, and there was little evidence of inter-particle or particle-substrate (steel plate) interactions at the particle densities used. Upon application of bulk acoustic waves at 3.7 MHz, the polystyrene particles levitated into the nodal plane (also called the levitation plane), as evidenced by the fast upward motion of all the particles from the bottom of the cell. The origin of the levitation force is well-known in the acoustics literature, and is generally attributed to the primary acoustic radiation force exerted on particles by sound propagation perpendicular to the substrate. 64 Since the acoustic pressure is at its minimum in the nodal plane, particles are trapped in that plane. The frequency range for levitating particles was between 3.5 MHz to 4 MHz, which was close to the calculated n=1 resonant frequency of the cell. When frequencies below or beyond that range were used, the particles remained at the bottom of the cell. Turning off the acoustic excitation resulted in sinking of the levitated particles.

Once in the nodal plane, both small (470 nm) and large (2 μm) spherical polystyrene particles showed acoustic streaming. At certain frequencies, within seconds to minutes, the particles formed circular or linear aggregates (termed ring and streak patterns, respectively, in the discussion below), as shown in Figure 4-3. It was hard to predict or control the shapes of these

aggregates, although varying the frequency could lead to the transformation from steak patterns to ring patterns, or vice versa. The collection of particles in patterns in the nodal plane of a bulk acoustic field has been reported before, and is generally considered to be due to the variation of the acoustic field in the lateral directions.57,65 Such variations can arise from near field effects or from higher dimensional acoustic modes.66, 67 Although the origin of these variations is not known in the present case, it appears that the particles follow the acoustic energy distribution in the nodal plane.

Figure 4-3. Typical patterns formed by polystyrene (PS) tracer particles in the nodal plane in a

3.7 MHz acoustic field. (a)-(c) are ring patterns, streak patterns and a dense aggregate formed by

470 nm diameter PS particles, respectively. (d)-(f) are the same types of patterns formed by 2 μm diameter PS particles. In these dark field images, the particles appear bright and the background is dark. (g) Cartoons showing the dimensions of the formed patterns as well as the nodes.

The ring diameters and distances between streaks were typically in the range of 200 μm, which corresponds to half the wavelength of the sound wave at the driving frequency. This indicates a correlation between the patterns and the acoustic nodal structures in the plane (Figure

4-3g). Although sharp resonance patterns are difficult to obtain in the nodal plane because of scattering and reflection of acoustic waves, under certain conditions localized nodal patterns can be formed and that explains the ring and streak patterns that formed at certain frequencies. One can draw a comparison between the patterns seen in Fig. 4-3 to nodal patterns formed by sand on a Chladni plate, which collects mobile particles at the acoustic nodes.68 Similarly, 2-D alignment of particles into rings and other more complicated structures has been experimentally demonstrated and theoretically modeled.52 It is worth noting that once the polymer microparticles were collected and aligned into rings or streaks, they showed only acoustic streaming with no evidence of powered rotation or directional motion in either the levitation plane or the vertical direction.

4.3.2 Metallic microrods

Suspensions of metallic micro-rods showed interesting differences from polymer spheres under the same conditions. In these experiments, the rods were typically 1 to 3 μm long and 300 nm in diameter. The rods were made of a single metal component (Au, Ru or Pt) or were axially segmented (AuRu or AuPt, with the two ends being different metals). Au, Ru and Pt rods behaved almost identically to each other, and this was also true for AuRu and AuPt bimetallic rods. Therefore for the convenience of the discussion, we focus on pure Au and axially segmented AuRu rods. When the acoustic field was turned on, the rods levitated and ring and/or streak patterns were formed, similar to those of polymer tracer particles. However a number of new behaviors (illustrated and summarized in Fig. 4-4), including powered autonomous motion, were also observed.

Figure 4-4. (a)-(c): Illustration of the kinds of motion (axial directional motion, in-plane rotation, chain assembly and axial spinning and pattern formation, especially ring patterns) of metal microrods in a 3.7 MHz acoustic field. AuRu rods (gold-silvery color in dark field) showed similar behavior to the Au rods, except that they moved with their Ru ends (the silvery end in the image) forward and aligned head-to-tail into chains. (d) and (e): Dark field images of typical chain structures and ring patterns formed by Au and AuRu rods. Note that the cartoons superimposed on (d) are intended to show the alignment of the rods and are not to scale or in proportion to the aspect ratio of the Au or AuRu rods.

Once in the levitation plane the metallic rods showed axial directional motion (Figure 4-

4b) at speeds as high as ~200 μm/s. It is important to note that this motion was not driven simply by fluid convection, as rods that were near each other in the fluid moved autonomously in different directions. Varying the amplitude of the acoustic wave can lead to faster or slower rod speed. The speed was a function of both the location of the rods in the levitation plane and the frequency of the acoustic wave. For example, at a driving frequency of 3.776 MHz, the rods near

the cell center showed very fast axial motion as well as in plane rotation ,while rods near the edge of the cell showed much slower motion. Therefore we identify 3.776 MHz as the resonance frequency for the cell center. It is important to note that even a slight deviation (a few kHz, about

1% of the frequency) away from the resonant frequency dramatically decreased the intensity of the rod motion. However tuning the frequency away from resonance for the cell center brought other parts in the cell into resonance and induced rapid movement of metal rods in those locations.

Although we could not distinguish in the optical microscope which end was moving forward for single component metal rods, the two ends of the bimetallic rods had clear optical contrast in dark field, from which we could infer that they were propelled with one end consistently forward. For example, in the case of AuRu rods, the directional motion was always with the Ru end (which appears silvery in the dark field) leading. This suggests that the asymmetry of composition or shape of the metal rods can lead to directional motion.

Directional motion of metal rods occurred everywhere in the levitation plane, even where rods were aggregated into ring or streak patterns (Figure 4-4c). As noted above, the metallic rods when levitated into the nodal plane also formed ring and streak patterns. However unlike the polymer spheres, which showed only acoustic streaming within these patterns, metallic rods moved along the edges of these patterns and particularly for the ring patterns orbited the center of the ring, with different rods orbiting clockwise and counter-clockwise. This indicates that the propulsion of the metallic rods in the acoustic field is independent of their aggregation into rings or streaks, i.e., that the aggregation of the rods into patterns did not stop their directional motion or change their direction. Additionally, the metallic rods not only formed a dense ring pattern, as polystyrene particles did, but also populated the inside of the ring, forming many concentric and less dense rings in which chains of rods orbited the center (see Figure 4-4e). At the centers of these rings, there was a smaller number of metal rods showing limited directional motion. As noted above for the case of polystyrene particles, the aggregation of metal rods into defined

structures in the levitation plane can be attributed to the distribution of the acoustic energy in that plane.

Within the rings or streaks formed by metallic rods we observed another unique behavior that was not seen with spherical polymer particles. The metal rods and their aggregates rotated rapidly about the axis of the rods and the spindle axis of the rod-shaped aggregates, respectively, as is illustrated in Figure 4-4a. In contrast, for 470 nm and 2 μm diameter polymer spheres, we observed the aggregation of particles into patterns, but no axial rotation. Due to the instrumental limitation of the camera used to record the videos (30 frames per second), the rotation speed of the metal rods or aggregates could not be accurately measured At present, this motion is not completely understood, but it has been reported that ultrasound irradiating metal particles and cylinders in suspension can excite elastic surface waves, or Rayleigh waves, at frequencies spanning form kHz to MHz depending on the nature of the metal. 69 Depending on the angle of the incident wave, in this case the standing wave in the levitation plane, the surface waves can have a helical shape with respect to the rod axis. 70 We hypothesize that the helical surface waves can drive the rotation of the metal rods, which in turn creates a vortex through hydrodynamic drag. It may also cause the in-plane rotation of metallic rods noted above (Figure 4-4b), since in that case the incident wave is in the vertical direction, not in the levitation plane as it is for rods rotating axially. It is important to note that Rayleigh waves are also present in the case of spheres, generating rotation by interaction with incident standing waves. This will help explain the chaining and rotation of gold microspheres, which will be discussed below. This effect was seen only for metallic particles and not for polymer particles, presumably because the elastic waves in polymers are dampened much more effectively because of the higher compressibility of polymers.

For ring patterns, the vortices always pointed to the inside of the ring in the sense that fluid was driven into the ring from above and out from below, regardless of which direction the rods were moving or where they were observed on the ring. This uniform flow pattern around the ring, concurrent with the axial movement of rods around the ring, indicates that the generation of

vortices and the axial propulsion of the metal rods have two distinct mechanisms and can be decoupled.

To examine more closely the fluid flow induced by the spinning metal rods as well as to study the interaction between the metal rods and passive tracer particles, we mixed metal rods with 470 nm polystyrene particles. The tracer particles were readily trapped by the vortex formed around the metal rods once the ring or streak patterns were established, and they were observed to orbit around the rod spindle axis. The hydrodynamic drag of the vortex extended many rod diameters into the fluid, and the vortex tended to become stronger as the spinning bundle increased in length and diameter. The motion of tracer particles in this experiment also confirmed the toroidal fluid pumping into and out of the ring. When not at the nodal lines, metal rods moving in directional motion were observed to scatter small polystyrene particles away.

The vortices generated by the metal rods lead to the self-assembly of the rods into chains, as illustrated in Figure 4-4a and d. The chaining occurred exclusively in the ring and streak patterns, and is believed to result (as described below) from a combination of several attractive and repulsive forces. Once two metal rods align, they continue to assemble with other rods, individual or chains, and form long chains. Interestingly, when two chains (or rods) traveling in opposite directions meet each other, they do not interfere with each other’s motion or assemble into growing chains. Instead they spiral around each other and continue in their original direction of motion; these directions are opposite along the chain axis, because all the rods are confined by the vortex drag force. This illustrates the strong integrity of the self-assembled chain structures.

Figure 4-5 schematically illustrates the self-assembly and interactions of chains formed by metal rods.

Figure 4-5. Illustration of chain assembly and directional motion of metal rods along the chains:

(a) two metal rods moving in the same direction along the ring interacts and form a spinning doublet. (b) two metal rods moving in opposite directions either brush against each other or meet each other head-to-head; (c) when a metal micro-rod meets a chain moving in the opposite direction, the rod brushes against the chain and the two parties continue separately.

We also observed polar chains formed by AuRu bimetallic rods (Figure 4-4a and d).

Each polar rod in these chains points in the same direction so that the chain has an

AuRu|AuRu|AuRu…structure. This head-to-tail assembly is not particularly surprising considering that the bimetallic rods always move with the same end forward (e.g. the Ru end for

AuRu rods), and only rods moving in the same direction can align into chains. As noted above, chains moving in opposite directions eventually pass each other without coalescing into a single chain.

4.3.3 Metallic spheres and polymeric rods

In order to better understand the effects of different materials and shapes in the ultrasonic field, we conducted control experiments with polymer (polypyrrole) rods and gold microspheres.

The behavior of these particles is summarized briefly in Table 4-1.

Table 4-1. Summary of behaviors of different samples in an acoustic field

Sample Pattern Directional Particle alignment into chains (Figure Aggregate formation* motion S11) spinning Polymer Yes No No, particles were loosely aligned into No spheres narrow aggregates Polymer Yes No No, particles were loosely aligned into Yes, but rod narrow bands weak Metallic Yes Some did** Yes, with clear attraction between Yes, fast spheres particles Metallic Yes Yes Yes, very regular chains were formed, Yes, fast rods clear attraction between particles observed *: Patterns formed by either polymer or metallic microparticles in an acoustic field are generally rings, streaks or dense aggregates.

**: A small percentage of gold microspheres showed fast directional motion in an acoustic field. It is likely that these gold particles were not perfectly spherical (as can be seen in

Figure S3), and that their asymmetric shapes induced directional motion as in the case of gold rods.

To summarize the results collected in Table 4-1, metal rods induced strong vortices when aligned and also showed strong axial directional motion, whereas spherical metal particles induced vortices but only rarely showed directional motion, which was possibly a consequence of some small shape asymmetry. Polymer particles, regardless of their shape, did not show directional motion or induce strong vortices. This supports the hypothesis that material and shape are important in inducing strong vortices and directional motion. In addition, the fact that polymer rods showed no directional motion but weak axial rotation when aligned supports the hypothesis

that axial rotation and directional motion are distinct behaviors that arise from different effects in the acoustic field.

Among the kinds of motion described above, axial propulsion is particularly interesting because it opens up the possibility of powering autonomous movement in a variety of media that are compatible with ultrasound. The speed of axial propulsion can be altered by changing the amplitude and the frequency of continuously applied acoustic energy. Another way to change the activity of the acoustic motors, and to estimate the magnitude of forces that cause levitation, chain formation, and axial motion, is by using pulsed ultrasound. Pulsed-mode experiments were carried out at the same frequency and amplitude as in the continuous experiments. The threshold for levitating rods at the onset of rotating motion was at a duty cycle of D0 = 0.04, which translates to a 1 kHz pulse repetition rate and N=150. By choosing different combinations of Tr and Tp, and therefore different D, it was possible to observe the onset of different kinds of movement. For example at a high D, which means a larger Tp and smaller Tr, metal rods levitate and show strong rotation. However when D is lowered, the activity of the rods decreased until at the threshold D0 the rods maintained levitation but showed little rotation. A duty cycle below the threshold D0 results in destabilization and sinking of the rods back to the bottom of the cell.

Video S5 demonstrates a pulse mode experiment with metal rods at a small pulse repetition rate.

4.3.4 Discussion of forces at work

The results from the pulsed-mode experiments help to quantify the forces at work in the different motions of the metal rods, especially the self-assembly into spinning chains (Figure 4-6).

First, there is a primary radiation force in the z direction (Fz) that levitates the rods and pushes them into the nodal plane at the center of the cell. Below the threshold duty cycle of D0= 0.04, metal rods were no longer levitated and began to sink. At this power, the levitation force balances the gravitational force (G), which is approximately 0.027 pN for 2 µm 300 nm gold rods.

Therefore, for experiments carried out with continuous ultrasound at the same instantaneous power, the levitation force in the z direction can be estimated to be 1/D0 0.027 pN = 0.75 pN.

Figure 4-6. Illustration of the forces experienced by a metal rod in an acoustic field during self- assembly into chains. Red and yellow colors denote forces that bring the rods closer and push them apart, respectively. Fz: the primary radiation force in the z direction; G: the gravitational force; Fp: the propulsion force; Fhydro: the hydrodynamic force from the vortex; Fe: the electrostatic force; Fxy: the transverse component of the primary radiation force in the levitation plane; FB: the Bjerknes force; FVW: the van der Waals force.

There is also a transverse component of that primary radiation force acting on the rods in the xy levitation plane (Fxy), which pushes them into nodal lines and forms the streak and ring patterns in the levitation/nodal plane. At low Reynolds numbers (~10-4 -10-5 for micro-rods moving at a few µm/s), this force is equal to the hydrodynamic drag force, which can be estimated from Eqn. 4-2.

( )

where μ is the dynamic viscosity of water, L is the length of the rods (2 μm), R is the radius (150 nm), and υ is the velocity of the rods that are being pushed to the nodal lines, which is as ~5 μm/s from video clips. From (4-2), the drag force calculated to be ~ 0.025 pN, which equals to the transverse primary radiation force Fxy. The 1-2 orders of magnitude difference between the

primary radiation force in the z direction (0.75 pN) and the xy direction (0.025 pN) is consistent with previous experiments in similar geometries. 71

The force that propels the metal rods along their axis (Fp) can also be estimated from Eqn.

4-2, only in this case the velocity υ can be as high as 200 μm/s, which corresponds to a force of

~1 pN. This force is about two orders of magnitude stronger than Fxy and is comparable to the primary radiation force in the z direction Fz. This suggests the axial propulsion of the metal micro-rods arises primarily from scattering of acoustic waves traveling in the z-direction. A more detailed discussion on the axial propulsion will be provided in the following section.

It is well known that for two particles in the same nodal plane there exists an attractive force between the particles that arises from the reflected wave from one particle acting on the other. This is known as the secondary radiation force, also called the Bjerknes force

(FB).Woodside et al. measured the Bjerknes force relative to the primary radiation force in the z direction for two 5.1 μm radius polystyrene particles and found that the maximum FB is

65 approximately two orders of magnitude weaker than the maximum Fz. Using their experiment as a guideline we estimate the average Bjerknes force between two metal rods to be the order of 10-2 pN, which is similar to the transverse component of the primary radiation force Fxy. We note that

2 FB scales as 1/D , where D is the distance between the particles. Therefore as the rods get closer to each other they experience a stronger FB.

Another attractive force is the Van der Waals force (FVW), which is significant only at short range. By approximating the particles as 1 μm diameter gold spheres, we estimate FVW on the order of 10-2 pN at D = 1 μm from the Eqn.4-3.

Here A is the Hamaker constant for gold (3.0×10-19 J), R is the radius of the particle (500 nm) and D is the distance between the particles. Since FVW is on the same order of FB, they play similar roles in bringing two rods together when they are relatively close.

For metal rods that have a negative zeta potential in water, there is additionally a longer- range electrostatic repulsive force (Fe). As detailed below, we compared the behavior of the metal rods in pure water and in solutions of high ionic strength in which the electrostatic attraction should be screened at distances greater than tens of nanometers. Because the behavior was similar in the two media, it appears that the effect of electrostatic repulsion in the chain assembly process is negligible.

Considering the magnitude and direction of these forces, we present the following scenario for the self-assembly of metal rods: two rods moving near the nodal line are pushed by the transverse primary radiation force (Fxy) so that they align on the nodal line, preferentially into one line so each rod is at the pressure minimum. When rods align within a distance of a few µm, the attractive Bjerknes (FB) and van der Waals (FVW) forces cause them to accelerate towards each other and form a chain. The spiral trajectory of the rods moving together and eventually connecting to form a spinning chain on the nodal line is a combination of the axially forward motion of the incoming rod and its circular revolution around the chain.

4.3.6 Mechanism of axial rod propulsion

At present, the axial motion of the metallic rods is not understood quantitatively, but some mechanisms can be eliminated based on control experiments. One of these is self- electrophoresis, which is one of the most important mechanisms for catalytic microparticle

72, 73 propulsion in the presence of chemical fuels such as H2O2. Because the generation of H2O2 in

74 water by ultrasound has been reported, it is conceivable that H2O2 generated at the rod surface could contribute to axial motion. However three experimental observations argue compellingly against this mechanism in the present case. The first one is that single-component rods, such as

Au and Ru, showed comparable directional motion to bimetallic AuRu rods; the former do not show fast chemically powered movement in H2O2 solutions whereas the latter do. The second

observation is that AuRu moved with the Ru end forward when powered by ultrasound and in the

72 opposite direction when powered by H2O2. We observed that these rods reversed their direction when an acoustic field was applied to a rod suspension in 5% H2O2 solution, indicating different mechanisms with and without the acoustic field. It is also well known that even low

concentrations of salts inhibit the self-electrophoretic movement of catalytic micromotors in H2O2.

8 However, we observed identical behavior when the acoustic experiments were conducted in 1

μM, 10 μM or 100 μM NaNO3 solutions, while the catalytic motors showed significantly decreased activity in 100 μM NaNO3. We also found that the activity of levitated metal rods in ultrasound was not significantly affected in a phosphate buffer saline (PBS) solution diluted 1:1 with water. The latter experiment illustrates the promise of using ultrasonic propulsion of metal rods in a biological environment.

A more plausible mechanism for the directional motion of metal rods in an acoustic field is based on the shape asymmetry of the rods. Microrods prepared by template electrodeposition typically have a concave or convex end instead of perfectly flat end. The pores in which the microrods are grown are small enough that the rod-wall interaction can lead to preferential growth along the wall. The unevenness of the surface on the rod end is made more complex by the kinetics of the metal deposition, since fast growth (high current density) produces rougher deposits while slower deposition tends to produce a smoother end surface.75, 76 Field emission

SEM images of the metal rods that were used in the acoustic experiments (Fig. 4-7) showed that regardless of the metals used, one end of the rod was always markedly concave while the other end was slightly convex to flat (Ru), fairly flat (Pt) or quite rugged (Au). The end where it was always concave was identified as the end grown immediately after deposition of the sacrificial silver layer, which is typically the first step in electrodepositing nanowires in AAO membranes.

Figure 4-7. Electron micrographs of Au (a) and AuRu (b) rods used in the ultrasonic propulsion experiments. For AuRu rods, the Au end is clearly concave and there is also some incidence of rod branching at the Au end. The Ru end is usually pointed or flat. Au rods typically have one concave end and one pointed or flat end.

The asymmetric shape of the metal rods can lead to an asymmetric distribution of the acoustic pressure from the scattering of the incident acoustic waves at the metal surface. The scattering of acoustic waves from concave shapes concentrates energy near the curvature, whereas convex shapes scatter radially and weaken the energy density near the curvature.

Therefore asymmetric shapes result in an uneven distribution of acoustic pressures in the fluid that is stronger at the concave end (Au end in AuRu rods), propelling the rods with the other end

(Ru) consistently forward. It is important to note that many studies have been made about scattering of acoustic waves by cylinders at ka > 1 (where k is the wave number and a is the cylinder diameter),70, 77 and only a few of them focus on cases where ka << 1, 78, 79which is the case in the present experiments.

The locally induced pressure gradient propels the metal rods in a similar way as the acoustic pressure gradient moves particles, a phenomenon sometimes called acoustophoresis. 48, 80

Since in the pressure gradient is generated locally and affects only the individual rods, we use the term self-acoustophoresis to describe this mechanism. We also examined AuPt bimetallic rods and the same mechanism could be applied to explain their direction of motion. Although we cannot identify which end leads the directional motion of single-component metal rods, the same concave features were found on those rods and therefore their motion can be explained by the same mechanism.

In order to further investigate this mechanism, we fabricated PtAu wires by electrodepositing Pt before Au segment. Rods made this way had a concave end at the Pt end. In this case, some of the PtAu rods moved with the Pt end forward while others moved with the Au end forward. The reversal of direction of some of the rods supports the hypothesis that the concave feature at the end of the rods is responsible for axial propulsion.

4.3.7 Ultrasound power and energy conversion efficiency of acoustic nanomotors

Finally, in order for ultrasonically propelled micromotors to be useful in biological environments, it is important to evaluate whether the power level is harmful to tissues or cells.

The output power from the function generator in a typical experiment is 250 mW. A fraction of this power is transmitted to the sample cell (0.2 cm2) and the rest is dissipated by the much larger steel plate (20 cm2) that is coupled to the transducer. If we assume that the energy is evenly distributed on the steel plate, then then power density is calculated to be 250 mW/20 cm2 = 12.5

mW/cm2. That power level is well below that of therapeutic ultrasound (several W/cm2 or higher) and that of diagnostic ultrasound (740 mW/cm2, the maximum ultrasonic power level allowed by

FDA for diagnostic purposes).81, 82 The use of such ultrasound power to propel motors is therefore considered safe for biological environments.

The energy conversion efficiency of the ultrasonically propelled nanomotors can be calculated by taking the ratio of the mechanical power output over the total acoustic power input of one microrod. The mechanical power can be calculated with Eqn. 2-6 to be on the order of 10-

16 W/rod. The acoustic power input can be estimated by assuming the energy is uniformly distributed over the nodal plane. Therefore the fraction of that energy absorbed by the metal microrod is on the order of 10-10 W/rod. A rough estimate of the energy efficiency of an acoustic nanomotor is therefore on the order of 10-6.

4.4 Modulation of the speed of acoustic motors via external parameters

4.4.1 Voltage modulation

In section 4.3.2 it was briefly mentioned that both the voltage and frequency of the sound wave signals from the function generator affect the motor behavior. Here a more systematic study of the effect of these two parameters is conducted to provide better understanding, as well as to demonstrate the capability of fine-tuning the motor speeds by varying output parameters from the function generator. This is potentially important for applications that require precise control over motor behaviors, such as drug delivery or minimally invasive surgeries.

First, motor behaviors at varying output voltages from the function generator were captured and tracked. The results are plotted in Fig. 4-8.

Figure 4-8. The average speed of acoustically driven micromotors increases quadratically with increasing applied voltage. The tracking data for motors at 8 V was considered abnormal and not used for fitting. The errors represent the standard deviation of the tracking results of multiple microrods at one particular voltage.

The quadratic relationship between the motor speed and the peak-to-peak voltage can be

80 understood in terms of the primary radiation force in the z direction, defined as :

where a is the particle radius, is the acoustic energy density, k is the wavenumber

(2πf/c, f being the frequency and c being the sound velocity), z is the distance between the particle and the acoustic node, and Φ is the acoustic contrast factor. Further, the acoustic energy density

83 was found to scale with the square of the peak to peak voltage applied:

Combining Eqn. 4-4 and 4-5, we see that the acoustic radiation force is proportional to the square of the voltage applied. This lends further support to the idea that the microrod in an ultrasonic standing wave is propelled by the scattering of the acoustic wave, as was proposed in section 4.3.6 as the foundation of the propulsion mechanism.

4.4.2 Frequency modulation

The motor behavior can be also modulated by tuning the frequency at which the sound wave propagates. As illustrated in Fig. 4-9, the speed of the motors increases with the frequency, reaching a peak speed at the resonance frequency, then decreases as frequency is increased beyond the resonance frequency.

Figure 4-8. The speed of acoustic nanomotors at various frequencies.

There is no satisfactory theory that explains the linear relationship between the motor speed and the frequency applied, although qualitatively we understand that at the resonance

frequency (when a standing wave is formed) the primary radiation force (section 4.3.4, also Eqn.

4-4), which is responsible for the propulsion of the microrods, is much stronger than it is off- resonance when waves can propagate only as traveling waves. 53 However the analysis is complicated because there exists a resonance frequency for the chamber (see the condition to form a standing wave in the chamber, Eqn. 4-1), for the transducer used (which has its own power profile that peaks at the resonance frequency, characterized by the Q factor), and the entire system (considering the coupling between the transducer and the medium, the modulation of the sound waves by the medium, etc.). Interpretation of the relationship presented in Fig. 4-9 therefore has to be carried out carefully, preferably with a full understanding of the interplay among the components constituting the acoustic chamber, which we currently lack. A more in- depth study of the relationship between motor speed and frequency is therefore needed for the development of the acoustic motor system. Although only at a preliminary level of understanding, controlling the acoustic motor speed via voltage and frequency has served as a first step towards applying this nanomotor system to more advanced functions and applications.

4.5 Interactions between acoustic motors and biological cells

4.5.1 Background

In this section I will provide some preliminary results on how acoustic motors interact with cells (HeLa cervical cancer cells84) in a biologically relevant environment. In addition, the interactions between acoustic motors and polystyrene beads of similar dimensions (~10 μm) will be presented and discussed, to serve as a comparison. The interaction between motors and HeLa cells is complicated and results in interesting phenomenon, while 10 μm polystyrene beads typically behave as rigid bodies and result in elastic collisions.

The ultrasonically driven metallic motors have a high tolerance level of ionic strength, unlike their chemically driven counterparts. In section 4.3.6 it has been shown that acoustic motors can retain a high level of activity in PBS buffer solution with an ionic strength close to 1 mol/L. In addition, the power output of these acoustic motors is one the order of 10-16 W/motor, with a force level of 1pN and a peak speed of 200 μm/s. Although a number of bio-medical functionalities such as minimally invasive surgery and drug delivery have been proposed for nano- and microscale autonomous motors, 32, 85-88 it is crucial that one considers the hostile environment in the human body towards foreign microscale particles. The high tolerance of salt, relatively high power, the safety of the material the motor is made of (gold) and its relatively small size (2-3 μm long and 300 nm in diameter) present possibilities for applying the acoustic motors discussed here to living organisms in a way that has never been demonstrated before.

In this section of Chapter 4 HeLa cells were used as representative human cells to study interactions with acoustically powered nanomotors. In addition to their convenience of growth and handling as an immortal cell line, HeLa cells are cancer cells and thus are a model for interaction of motors with tumor cells. In the clinical treatment of cancer there are many obstacles that a motor would have to overcome even to reach the cancer cell, including various screening process employed by the human body and the high interstitial fluid pressure at the center of solid tumors.85, 86 Nevertheless, the goal of the last step of any drug delivery is an effective interaction between the agent and the target cells or sub-cellular organelle. This is essential to biomedical applications such as the delivery of the drugs, photothermal therapy and mechanical destruction of cancer cells. Cancer cells are covered with proteins and receptors, and their fast growth leads to varying life cycles from one cell to another. All of these add to the complexity of the discussion of the interaction between motors and cancer cells. In this section I will provide some experimental results that on one hand illustrate the difficulty, and on the other hand demonstrate the possibility to overcome such complexity.

4.5.2 Interactions between acoustic nanomotors and polystyrene beads

Polystyrene microspheres (or PS beads) were used to study the interaction between microparticles and acoustic motors. When suspended together with acoustic motors (gold microrods, ~3 μm long and ~ 300 nm in diameter) and in a standing acoustic wave, PS spheres and motors levitate to the center of the chamber and start to interact. Because the density of PS beads and gold microrods are substantially different, when they levitate they populate two parallel planes in the z direction with gold on the plane below. The inter-plane distance is estimated to be

~1 μm, however an exact measurement is not yet available due to instrumental limitations. The acoustic and hydrodynamic interaction between PS beads and gold motors are usually strong enough to cause them to respond to each other even though they are in two different planes.

In chapter 4.3 the interactions between metallic acoustic motors and PS beads of 470 nm and 2 μm diameter have been described in detail. To summarize briefly, these relatively small PS beads are readily trapped by the vortices around the spinning metallic microrods at the nodal lines.

On the other hand, metallic microrods undergoing fast axial motion push away PS beads.

However the mechanism of this scattering effect is still under investigation. Both acoustic scattering and hydrodynamic interactions could contribute. Nevertheless the repulsive force between acoustic motors in axial motion and PS beads prevent them from being in physical contact with each other.

Large PS beads (10 μm) respond to the acoustic motors in a noticeably different way, mainly because the size, mass, and drag force of these PS beads cause the response to be much less intense. For example, when acoustic motors move close to 10 μm PS beads, the beads barely move and the motors usually change their trajectory by either moving in a new direction or completely reversing, in a trajectory that resembles an near-elastic collision (Fig. 4-10). In addition, although large PS beads are also subject to hydrodynamic drag when they are around spinning metal rods at the nodal lines, they cannot completely synchronize with the spinning

microrods due to their large size and consequently strong viscous drag force. What is more, when metal acoustic motors move in a dense 2D aggregate of large PS beads, the motors push away the beads slightly to create a path between the beads and glide through, almost without a change in their speed. This is interesting especially in comparison to the fate of motors navigating through a

2D aggregate of HeLa cells (discussed later).

Figure 4-9. Interaction between acoustic motors and 10 μm PS beads. The acoustic nanomotor

(light grey, bottom left at 0 s) collides with a PS bead and changes its trajectory (moving to the right at 0.3 s). Scale bar: 10 μm. Images were taken in bright field.

In summary, the PS beads respond to the acoustic motors in a passive way. When the beads are relatively small, the scattered acoustic wave from the metal rod surface is sufficient to affect the motion of the PS beads. When the beads are large, however, they undergo momentum transfer with incoming acoustic nanomotors that minimally affects the large PS beads due to a large drag resistance that scales with the size of the beads. A quantitative study of this momentum transfer is underway through collaboration with NIST, but the results are currently too preliminary for publication in this dissertation.

4.5.3 Interaction between acoustic motors and HeLa cells in a mixed suspension

In order to study the interactions between acoustic nanomotors and HeLa cells, they were mixed in PBS solution and the mixed suspension was added to an acoustic chamber with a

resonance frequency of ~2.4MHz. When the acoustic field is turned on, metallic microrods and

HeLa cells alike readily levitate into the nodal plane. Due to their large size, HeLa cells respond to the acoustic radiation force strongly and quickly aggregate at the pressure node (Radiation force scales as the third power of the radius of the particle. see Eqn.4-4), which typically is at the center of the acoustic chamber at the resonance frequency. It is worth noting that the position of the aggregate of HeLa cells is particularly sensitive to the ultrasonic frequency, and can shift abruptly and significantly by varying the frequency slightly. This can cause technical difficulties when examining the behaviors of acoustic motors as well as HeLa cells at varying ultrasonic frequencies. In addition, an amplifier can also be used to increase the acoustic power. However at elevated power levels acoustic streaming becomes significant and convection can strongly affect the positions of HeLa cells and acoustic motors. The biological effect of acoustic streaming on the viability of the HeLa cells remains to be investigated. Therefore the observations that will be described below were conducted under conditions where acoustic streaming was not significant.

The interaction between gold acoustic motors and HeLa cells in an ultrasonic standing wave is dominated by the surfaces of the two particles. Specifically, significant binding of gold microrods on the HeLa cell surface was observed (Fig. 4-11). This binding was fast, typically occurring immediately after these two particles came into contact. There is no orientation dependence of the binding; the acoustic motors can bind with their tips or sides, and binding occurs for motors moving in either direction. In addition the attachment of a gold microrod to the surface of a HeLa cell does not noticeably affect subsequent binding of more microrods.

Figure 4-10. Binding between acoustic nanomotors and HeLa cells in a mixed suspension in an acoustic field.

This strong binding could be a result of the high ionic strength (~ 0.2 mol/L) of the solution being used. At such high ionic strength colloidal particles show significant aggregation due to the collapse of the electrical double layer and consequently the disappearance of long range electrostatic repulsion. Therefore although both the gold microrods and HeLa cells carry negative surface charges (ζAu~ -40 mV, see chapter 2. Cells typically have negative surface charges 87), at such high ionic strength they can move much closer to each other without being repelled by electrostatic forces and experience an attractive van der Waals force.

The other contribution to binding could come from gold-sulfur or gold-nitrogen dative bonds formed between the gold surface and the proteins on the surface of HeLa cells. We have also noticed a slightly lower binding probability of gold microrods to dead HeLa cells, which can be attributed to the change of protein activity on cell surface after cell death. In addition ruthenium microrods of similar shapes and dimensions bind less to the HeLa cells than gold rods,

indicating the chemistry of the microrod surface affects the binding, which is consistent with the idea of strong Au-S or Au-N interactions. The combination of the van der Waals force and coordinate covalent bonding therefore leads to strong binding between gold microrods and HeLa cells at high ionic strength. A statistical analysis of the binding event under various conditions is needed to clarify the binding mechanism.

Interestingly the aggregation between gold microrods and HeLa cells in an acoustic field is not permanent, unlike the aggregation of colloidal particles at high ionic strength. Gold microrods bound to the HeLa cell surface could be released and move freely, until they attach to another HeLa cell. This binding-release-rebinding cycle could repeat many times, and it can be attributed to the active nature of the gold microrods. In other words, the force equilibrium between attractive binding forces and the propulsion force that is moving the microrod away can be broken. In addition the Brownian motion that causes constant positional shifts of the gold microrods could also contribute to the eventual separation of the microrods and HeLa cells.

Although a more quantitative study is needed to understand this reversible binding, we have qualitatively observed that increasing the acoustic power leads to higher probability of gold microrods hopping away from the HeLa cells they originally attached to.

Due to the strong binding between gold microrods and HeLa cells, the activity of acoustic motors within a 2D matrix of HeLa cells is greatly limited. Although the microrods can be released from the cell surface, they are usually captured by the nearby cells before they move far.

Hopping of gold microrods between HeLa cells therefore occurs intermittently, with microrods spending the majority of the time bound to the cell surface and much less time traveling between cells. We note that reduced activity in cancer cell matrix is a common problem for drug delivery into tumosr, and is more pronounced in tumors than in a 2D matrix of cancer cells due to the existence of highly interconnected collagen fibers.85 Acoustic motors are potentially superior to passive particles being delivered to the tumors because motors can actively migrate via the

intermittent hopping mechanism, whearas passive particles typically lose their ability to move once they are bound to the cell surface.

On the other hand, the intermittent hopping of gold microrods among multiple HeLa cells can prove useful if exploited properly. For example the microrods might be functionalized to be able to slowly release drugs, and drugs could therefore be efficiently distributed among many cancer cells because of slow migration. Moreover, the gold microrods can be decorated with photothermal nanoparticles that could heat cancer cells when the microrods are attached to them.

In this case being attached to the cancer cell actually helps the therapy to be effective.

In summary the interaction between acoustic nanomotors and HeLa cells in a mixed suspension in an acoustic field is dominated by the strong binding between gold and cell surfaces.

Two binding mechanisms were proposed: van der Waals attraction winning over electrostatic repulsion at high ionic strength, and strong gold-sulfur and/or gold-nitrogen bonds. Migration of gold acoustic motors through a dense 2D aggregate of HeLa cells proved to be difficult, although intermittent hopping from cell to cell by gold microrods were observed. This hopping is attributed to the competition between the propulsion force and the binding forces.

4.5.4 Interactions between acoustic motors and HeLa cells after incubation

In this section, instead of exposing a mixed suspension of gold acoustic motors and HeLa cells to acoustic fields, they were first incubated together for 6 to 48 hrs. Incubation of HeLa cells with gold microrods leads to significant cell uptake of gold microrods. Although quantitative results are not available, a qualitative estimate suggests that longer incubation time leads to more uptake of gold microrods in HeLa cells. For example after 6 hrs of incubation most of the gold microrods were either attached to the cell surface or suspended freely in the solution, while after

48 hrs most of the rods had been internalized. Regardless of the incubation time, cells and gold

microrods could levitate to the central nodal plane upon exposure to acoustic fields at the proper frequency.

In the nodal plane, cells incubated with gold microrods for different durations behaved differently. The sample of 6 hrs incubation demonstrated typical microrod-cell interactions: microrods move by acoustic propulsion as well as bind to the cell surface, and cells migrate towards nodal points. On the other hand, samples of longer incubation times (24 hrs and 48 hrs) contained mostly HeLa cells with gold microrods internalized. Interestingly these gold microrods, although trapped inside cells, are still very responsive to the acoustic fields and remain active.

Both directional motion and spinning of these gold microrods can be observed to occur inside the

HeLa cells. Figure 4-12 presents time lapse snapshots of the motion of a gold microrod inside a

eLa cell at an average speed of ~ 20 μm/s.

Figure 4-12. Gold microrods remain active inside HeLa cells. 6 snapshots of 0.1 s intervals demonstrate the motion of one gold microrod (white arrow) inside a HeLa cell. Two grey particles (discussed below) are circled and a blow-up is shown in the inset. Scale bar: 10 μm.

Three key observations are particularly worth noting.

1. Cell uptake of gold microrods differs greatly from one cell to another. It is common to see one cell with more than 10 microrods internalized being surrounded by cells with hardly any microrods inside. There are two possible explanations for this effect. First, the microrods may be inhomogeneously distributed over the cells during the incubation period, before the cells are compressed together at the acoustic nodes for observation of powered motion. Second, different cells might be at different phases of their life cycles, thus exhibiting different tendencies to internalize foreign objects.

2. There appear to be numerous dark microparticles in the cells that interact with active gold microrods in a way similar to polystyrene tracer particles of similar sizes (Fig. 4-12, inset). The exact nature of these dark objects remains unknown at this point, however it is fair to assume that they are subcellular organelles. This raises the interesting question of what kind of mechanical or biological responses are generated by the cell as a result of its interactions with microrods inside.

3. It is clear that the active nanomotors inside cells, although capable of reaching speeds as high as ~ 100 μm/s, are bound by the cell membrane. This is consistent with our observation that metallic acoustic nanomotors outside cells cannot penetrate cell membranes. This suggests that cell membranes can withstand forces on the orders of 1pN, which corresponds to a pressure on the order of 10 Pa. n the other hand, it has been demonstrated that bubble propelled nanojets

(600 nm in diameter and 10 μm long) moving at ~ 200 μm/s could drill into eLa cells.88 In this case the penetration was facilitated by the cork-screw rotation of the nanojets. Therefore magnetic or acoustic spinning could be potentially implemented in the case of acoustic nanomotors, enabling them to penetrate cells.

The mechanism of cell uptake of micron sized gold microrods remains unclear. It is widely accepted that for nanoparticles around 100 nm or smaller, receptor mediated endocytosis is the main mechanism for cell uptake, while particles larger than 500 nm are believed to be internalized primarily through phagocytosis.89-92 However HeLa cells are typically considered to be non-phagocytosing cells, unlike macrophages. Gratton et al. studied the effect of particle shape,

size and surface charge on internalization by HeLa cells, and also discovered that HeLa cells readily internalize particles with sizes up to a few micrometers.93 They determined that claritin- mediated and caveolae-mediated endocytosis as well as macropinocytosis are involved with the particle internalization process. In addition they discovered that rod shaped particles with relatively high aspect ratios demonstrated higher cell uptake. Their findings are consistent with our experiments, in which gold microrods with negative surface charges exhibited strong cell internalization, whereas ordinarily positively charged particles are preferentially internalized by cells with negatively charged surfaces. It has been reported that serum helps the cell uptake of particles of smaller sizes through receptor-mediated endocytosis. 94 However the effect of serum in the cell culture medium during the incubation on the cell uptake of gold microrods was determined to be insignificant, because cells were able to internalize gold microrods with or without serum. This lends support to mechanisms other than receptor-mediated endocytosis for cell uptake of gold microrods in our experiments.

To briefly summarize, HeLa cells readily uptake gold microrods when they are incubated together for a prolonged period of time (≥ 24 hrs). nce inside the cells, metallic microrods respond to the acoustic fields and demonstrate both directional motion and spinning. Clear mechanical interaction between the gold microrods internalized and HeLa cells have been observed, and biological interactions are suspected. These observations mark the first time that artificial nanomotors have been delivered into cells while maintaining their activity. Taking advantage of the opportunity offered by active nanomotors inside the cells, intracellular functions and mechano-biology coupling can be studied from a unique angle. In addition, functionalities such as sensing, drug delivery or phototherapy can be added to the nanomotors, enabling them to carry out various operations directly inside the cells, thus opening up a new and exciting route for possible biomedical applications.

4.6 Conclusions

We have demonstrated that MHz frequency acoustic waves can propel, align, rotate and assemble metallic micro-rods in water. Control experiments with polymer particles and metal spheres lend support to the hypothesis that shape and material play a critical role in the directional motion and the generation of strong vortices along the axis of aligned metal rods. Based on observations with template-grown homogeneous and bimetallic microrods, it is likely that shape asymmetry, specifically the curvature at the ends of the micro-rods, leads to the directional motion by a self-acoustophoresis mechanism. The speed of the acoustic nanomotors shows linear and quadratic relationship with frequency and voltage of the ultrasound wave signal, respectively.

When mixed with polystyrene tracer particles, acoustic nanomotors significantly affect the motion of small PS particles, yet cause little change to the trajectory of large (10 μm) PS particles.

However when mixed with HeLa cells gold microrods in acoustic fields were shown to significantly bind to the cell surface, possibly due to a combination of van der Waals attraction at high ionic strength and specific gold-sulfur and gold-nitrogen bonds. Interestingly when HeLa cells were incubated with gold microrods for an extended period of time, gold microrods were internalized by cells and demonstrated slightly reduced activity within cells. The significance of our discoveries of ultrasonically driven metallic nanomotors as well as motor-cell interactions lies in the possibility of driving and controlling micromachines in biologically relevant environments using ultrasound.

4.7 References

1. Mirkovic, T.; Zacharia, N. S.; Scholes, G. D.; Ozin, G. A., Fuel for Thought: Chemically Powered Nanomotors Out-Swim Nature’s Flagellated Bacteria. ACS Nano 2010, 4 (4), 1782-1789. 2. Wang, J.; Manesh, K. M., Motion Control at the Nanoscale. Small 2010, 6 (3), 338-345. 3. Mallouk, T. E.; Sen, A., Powering nanorobots. Sci Am 2009, (May), 72-77. 4. Liu, R.; Sen, A., Autonomous Nanomotor Based on Copper–Platinum Segmented Nanobattery. J Am Chem Soc 2011, 133 (50), 20064-20067.

5. Pantarotto, D.; Browne, W. R.; Feringa, B. L., Autonomous propulsion of carbon nanotubes powered by a multienzyme ensemble. Chem Commun (Camb) 2008, (13), 1533-5. 6. Mano, N.; Heller, A., Bioelectrochemical Propulsion. J Am Chem Soc 2005, 127 (33), 11574-11575. 7. Kline, T. R.; Paxton, W. F.; Mallouk, T. E.; Sen, A., Catalytic Nanomotors: Remote- Controlled Autonomous Movement of Striped Metallic Nanorods. Angew. Chem. 2005, 117 (5), 754-756. 8. Paxton, W. F.; Baker, P. T.; Kline, T. R.; Wang, Y.; Mallouk, T. E.; Sen, A., Catalytically Induced Electrokinetics for Motors and Micropumps. J Am Chem Soc 2006, 128 (46), 14881-14888. 9. Wu, J.; Balasubramanian, S.; Kagan, D.; Manesh, K. M.; Campuzano, S.; Wang, J., Motion-based DNA detection using catalytic nanomotors. Nat Commun 2010, 1, 36. 10. Zhang, L.; Abbott, J. J.; Dong, L.; Peyer, K. E.; Kratochvil, B. E.; Zhang, H.; Bergeles, C.; Nelson, B. J., Characterizing the Swimming Properties of Artificial Bacterial Flagella. Nano Lett 2009, 9 (10), 3663-3667. 11. Ghosh, A.; Fischer, P., Controlled Propulsion of Artificial Magnetic Nanostructured Propellers. Nano Lett 2009, 9 (6), 2243-2245. 12. Tottori, S.; Zhang, L.; Qiu, F.; Krawczyk, K. K.; Franco-Obregon, A.; Nelson, B. J., Magnetic helical micromachines: fabrication, controlled swimming, and cargo transport. Adv Mater 2012, 24 (6), 811-6. 13. Gao, W.; Sattayasamitsathit, S.; Manesh, K. M.; Weihs, D.; Wang, J., Magnetically Powered Flexible Metal Nanowire Motors. J Am Chem Soc 2010, 132 (41), 14403-14405. 14. Dreyfus, R.; Baudry, J.; Roper, M. L.; Fermigier, M.; Stone, H. A.; Bibette, J., Microscopic artificial swimmers. Nature 2005, 437 (7060), 862-865. 15. Zhang, L.; Petit, T.; Lu, Y.; Kratochvil, B. E.; Peyer, K. E.; Pei, R.; Lou, J.; Nelson, B. J., Controlled Propulsion and Cargo Transport of Rotating Nickel Nanowires near a Patterned Solid Surface. ACS Nano 2010, 4 (10), 6228-6234. 16. Ogrin, F. Y.; Petrov, P. G.; Winlove, C. P., Ferromagnetic Microswimmers. Phys. Rev. Lett. 2008, 100 (21), 218102. 17. Calvo-Marzal, P.; Sattayasamitsathit, S.; Balasubramanian, S.; Windmiller, J. R.; Dao, C.; Wang, J., Propulsion of nanowire diodes. Chem. Commun. 2010, 46 (10), 1623-1624. 18. Chang, S. T.; Paunov, V. N.; Petsev, D. N.; Velev, O. D., Remotely powered self- propelling particles and micropumps based on miniature diodes. Nat Mater 2007, 6 (3), 235-240. 19. Hong, Y.; Diaz, M.; Córdova-Figueroa, U. M.; Sen, A., Light-Driven Titanium-Dioxide- Based Reversible Microfireworks and Micromotor/Micropump Systems. Adv. Funct. Mater. 2010, 20 (10), 1568-1576. 20. Liu, M.; Zentgraf, T.; Liu, Y.; Bartal, G.; Zhang, X., Light-driven nanoscale plasmonic motors. Nat Nano 2010, 5 (8), 570-573. 21. Ibele, M.; Mallouk, T. E.; Sen, A., Schooling Behavior of Light-Powered Autonomous Micromotors in Water. Angew. Chem. Int. Ed. 2009, 48 (18), 3308-3312. 22. Abid, J. P.; Frigoli, M.; Pansu, R.; Szeftel, J.; Zyss, J.; Larpent, C.; Brasselet, S., Light- driven directed motion of azobenzene-coated polymer nanoparticles in an aqueous medium. Langmuir 2011, 27 (13), 7967-71. 23. Stock, C.; Heureux, N.; Browne, W. R.; Feringa, B. L., Autonomous Movement of Silica and Glass Micro-Objects Based on a Catalytic Molecular Propulsion System. Chem-Eur J 2008, 14 (10), 3146-3153. 24. Gibbs, J. G.; Zhao, Y. P., Autonomously motile catalytic nanomotors by bubble propulsion. Appl. Phys. Lett. 2009, 94 (16), 163104-3. 25. Solovev, A. A.; Mei, Y.; Bermúdez Ureña, E.; Huang, G.; Schmidt, O. G., Catalytic Microtubular Jet Engines Self-Propelled by Accumulated Gas Bubbles. Small 2009, 5 (14), 1688- 1692.

26. Gao, W.; Sattayasamitsathit, S.; Orozco, J.; Wang, J., Highly Efficient Catalytic Microengines: Template Electrosynthesis of Polyaniline/Platinum Microtubes. J Am Chem Soc 2011, 133 (31), 11862-11864. 27. Pavlick, R. A.; Sengupta, S.; McFadden, T.; Zhang, H.; Sen, A., A Polymerization- Powered Motor. Angew. Chem. Int. Ed. 2011, 50 (40), 9374-9377. 28. Golestanian, R.; Liverpool, T. B.; Ajdari, A., Propulsion of a Molecular Machine by Asymmetric Distribution of Reaction Products. Phys. Rev. Lett. 2005, 94 (22), 220801. 29. Howse, J. R.; Jones, R. A. L.; Ryan, A. J.; Gough, T.; Vafabakhsh, R.; Golestanian, R., Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk. Phys. Rev. Lett. 2007, 99 (4), 048102. 30. Campuzano, S.; Orozco, J.; Kagan, D.; Guix, M.; Gao, W.; Sattayasamitsathit, S.; Claussen, J. C.; Merkoçi, A.; Wang, J., Bacterial Isolation by Lectin-Modified Microengines. Nano Lett 2011, 12 (1), 396-401. 31. Sundararajan, S.; Lammert, P. E.; Zudans, A. W.; Crespi, V. H.; Sen, A., Catalytic Motors for Transport of Colloidal Cargo. Nano Lett 2008, 8 (5), 1271-1276. 32. Balasubramanian, S.; Kagan, D.; Jack Hu, C.-M.; Campuzano, S.; Lobo-Castañon, M. J.; Lim, N.; Kang, D. Y.; Zimmerman, M.; Zhang, L.; Wang, J., Micromachine-Enabled Capture and Isolation of Cancer Cells in Complex Media. Angew. Chem. Int. Ed. 2011, 50 (18), 4161-4164. 33. Burdick, J.; Laocharoensuk, R.; Wheat, P. M.; Posner, J. D.; Wang, J., Synthetic Nanomotors in Microchannel Networks: Directional Microchip Motion and Controlled Manipulation of Cargo. J Am Chem Soc 2008, 130 (26), 8164-8165. 34. Hong, Y.; Blackman, N. M. K.; Kopp, N. D.; Sen, A.; Velegol, D., Chemotaxis of Nonbiological Colloidal Rods. Phys. Rev. Lett. 2007, 99 (17), 178103. 35. Kagan, D.; Balasubramanian, S.; Wang, J., Chemically Triggered Swarming of Gold Microparticles. Angew. Chem. Int. Ed. 2011, 50 (2), 503-506. 36. Campuzano, S.; Kagan, D.; Orozco, J.; Wang, J., Motion-driven sensing and biosensing using electrochemically propelled nanomotors. Analyst 2011, 136 (22), 4621-4630. 37. Jun, I.-K.; Hess, H., A Biomimetic, Self-Pumping Membrane. Adv. Mater. 2010, 22 (43), 4823-4825. 38. Zhang, H.; Yeung, K.; Robbins, J. S.; Pavlick, R. A.; Wu, M.; Liu, R.; Sen, A.; Phillips, S. T., Self-Powered Microscale Pumps Based on Analyte-Initiated Depolymerization Reactions. Angew. Chem. Int. Ed. 2012, 51 (10), 2400-2404. 39. Ozin, G. A.; Manners, I.; Fournier-Bidoz, S.; Arsenault, A., Dream Nanomachines. Adv. Mater. 2005, 17 (24), 3011-3018. 40. Ebbens, S. J.; Howse, J. R., In pursuit of propulsion at the nanoscale. Soft Matter 2010, 6 (4), 726. 41. Erikson, K. R.; Fry, F. J.; Jones, J. P., Ultrasound in Medicine-A Review. IEEE Transactions on Sonics and Ultrasonics 1974, 21 (3), 144-170. 42. Ziskin, M. C.; Petitti, D. B., Epidemiology of human exposure to ultrasound: A critical review. Ultrasound in Medicine & Biology 1988, 14 (2), 91-96. 43. Litvak, E.; Foster, K. R.; Repacholi, M. H., Health and safety implications of exposure to electromagnetic fields in the frequency range 300 Hz to 10 MHz. Bioelectromagnetics 2002, 23 (1), 68-82. 44. Kundt, A., Lehman, O., Longitudinal vibrations and acoustic figures in cylindrical columns of liquids. Annal Physik 1874, (153), 1. 45. King, L. V., On the acoustic radiation pressure on spheres. Proc R. Soc. London 1934, a147, 212-40. 46. Rayleigh, J. W., On the pressure of vibrations. Philosophical Magazine 1902, 3, 338-46. 47. Yosioka, K., Kawasima, Y., Acoustic radiation pressure on a compressible sphere. Acustica 1955, 5, 167-73.

48. Shi, J.; Ahmed, D.; Mao, X.; Lin, S.-C. S.; Lawit, A.; Huang, T. J., Acoustic tweezers: patterning cells and microparticles using standing surface acoustic waves (SSAW). Lab Chip 2009, 9 (20), 2890-2895. 49. Wood, C. D.; Evans, S. D.; Cunningham, J. E.; O'Rorke, R.; Walti, C.; Davies, A. G., Alignment of particles in microfluidic systems using standing surface acoustic waves. Appl. Phys. Lett. 2008, 92 (4), 044104-3. 50. Haake, A.; Dual, J., Contactless micromanipulation of small particles by an ultrasound field excited by a vibrating body. J. Acoust. Soc. Am. 2005, 117 (5), 2752-2760. 51. Lee, W.; Amini, H.; Stone, H. A.; Di Carlo, D., Dynamic self-assembly and control of microfluidic particle crystals. Proc Natl Acad Sci U S A 2010, 107 (52), 22413-8. 52. Oberti, S.; Neild, A.; Dual, J., Manipulation of micrometer sized particles within a micromachined fluidic device to form two-dimensional patterns using ultrasound. J. Acoust. Soc. Am. 2007, 121 (2), 778-785. 53. Friend, J.; Yeo, L. Y., Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics. Rev Mod Phys 2011, 83 (2), 647-704. 54. Wang, Z.; Zhe, J., Recent advances in particle and droplet manipulation for lab-on-a-chip devices based on surface acoustic waves. Lab Chip 2011, 11 (7), 1280-1285. 55. Oberti, S.; Möller, D.; Neild, A.; Dual, J.; Beyeler, F.; Nelson, B. J.; Gutmann, S., Strategies for single particle manipulation using acoustic and flow fields. Ultrasonics 2010, 50 (2), 247-257. 56. Shi, J.; Yazdi, S.; Steven Lin, S.-C.; Ding, X.; Chiang, I. K.; Sharp, K.; Huang, T. J., Three-dimensional continuous particle focusing in a microfluidic channel via standing surface acoustic waves (SSAW). Lab Chip 2011, 11 (14), 2319-2324. 57. Martyn Hill, N. R. H., Ultrasonic Particle Manipulation. In Microfluidic Technologies for Miniaturized Analysis Systems, Steffen Hardt, F. S., Ed. Springer: New York, 2007; pp 357-392. 58. Lim, W. P.; Yao, K.; Chen, Y., Alignment of Carbon Nanotubes by Acoustic Manipulation in a Fluidic Medium. J. Phys. Chem. C 2007, 111 (45), 16802-16807. 59. Kong, X. H.; Deneke, C.; Schmidt, H.; Thurmer, D. J.; Ji, H. X.; Bauer, M.; Schmidt, O. G., Surface acoustic wave mediated dielectrophoretic alignment of rolled-up microtubes in microfluidic systems. Appl. Phys. Lett. 2010, 96 (13), 134105-3. 60. Smorodin, T.; Beierlein, U.; Ebbecke, J.; Wixforth, A., Surface-Acoustic-Wave- Enhanced Alignment of Thiolated Carbon Nanotubes on Gold Electrodes. Small 2005, 1 (12), 1188-1190. 61. Shilton, R. J.; Glass, N. R.; Chan, P.; Yeo, L. Y.; Friend, J. R., Rotational microfluidic motor for on-chip microcentrifugation. Appl. Phys. Lett. 2011, 98 (25). 62. Hu, J.; Tay, C.; Cai, Y.; Du, J., Controlled rotation of sound-trapped small particles by an acoustic needle. Appl. Phys. Lett. 2005, 87 (9), 094104-3. 63. Bazou, D.; Castro, A.; Hoyos, M., Controlled cell aggregation in a pulsed acoustic field. Ultrasonics, in press. 64. Lierke, E. G., Acoustic levitation - A comprehensive survey of principles and applications. Acustica 1996, 82 (2), 220-237. 65. Woodside, S. M.; Bowen, B. D.; Piret, J. M., Measurement of ultrasonic forces for particle–liquid separations. AlChE J. 1997, 43 (7), 1727-1736. 66. Townsend, R. J.; Hill, M.; Harris, N. R.; White, N. M., Investigation of two-dimensional acoustic resonant modes in a particle separator. Ultrasonics 2006, 44 Suppl 1 (0), e467-71. 67. Lilliehorn, T.; Simu, U.; Nilsson, M.; Almqvist, M.; Stepinski, T.; Laurell, T.; Nilsson, J.; Johansson, S., Trapping of microparticles in the near field of an ultrasonic transducer. Ultrasonics 2005, 43 (5), 293-303. 68. Jensen, H. C., Production of Chladni Figures on Vibrating Plates Using Continuous Excitation. Am. J. Phys 1955, 23 (8), 503-505.

69. Hobæk, H.; Nesse, T. L., Scattering from spheres and cylinders - revisited. In 29th Scandinavian Symposium of physical acoustics, Norwegian Physical Society: Oslo, 2006. 70. Bao, X.-L.; Cao, H.; Uberall, H., Resonances and surface waves in the scattering of an obliquely incident acoustic field by an infinite elastic cylinder. J. Acoust. Soc. Am. 1990, 87 (1), 106-110. 71. Spengler, J. F.; Coakley, W. T.; Christensen, K. T., Microstreaming effects on particle concentration in an ultrasonic standing wave. AlChE J. 2003, 49 (11), 2773-2782. 72. Wang, Y.; Hernandez, R. M.; Bartlett, D. J.; Bingham, J. M.; Kline, T. R.; Sen, A.; Mallouk, T. E., Bipolar Electrochemical Mechanism for the Propulsion of Catalytic Nanomotors in ydrogen Peroxide Solutions†. Langmuir 2006, 22 (25), 10451-10456. 73. Moran, J. L.; Posner, J. D., Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis. J. Fluid Mech. 2011, 680, 31-66. 74. Anbar, M.; Pecht, I., On the Sonochemical Formation of Hydrogen Peroxide in Water. J. Phys. Chem. 1964, 68 (2), 352-355. 75. Banholzer, M. J.; Li, S.; Ketter, J. B.; Rozkiewicz, D. I.; Schatz, G. C.; Mirkin, C. A., Electrochemical Approach to and the Physical Consequences of Preparing Nanostructures from Gold Nanorods with Smooth Ends. J. Phys. Chem. C 2008, 112 (40), 15729-15734. 76. DaSilva, M.; Schneider, M. M.; Wood, D. S.; Kim, B.-J.; Stach, E. A.; Sands, T. D., The Use of Polyethyleneimine to Control the Growth-Front Morphology of Electrochemically Deposited Gold Nanowires for Engineered Nanogap Electrodes. Small 2009, 5 (21), 2387-2391. 77. Ye, Z., A novel approach to sound scattering by cylinders of finite length. J Acoust Soc Am 1997, 102 (2), 877-884. 78. Honarvar, F.; Enjilela, E.; Sinclair, A. N., Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder. Ultrasonics 2011, 51 (2), 238-244. 79. Mitri, F. G., Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder. Ultrasonics 2010, 50 (7), 675-682. 80. Lenshof, A.; Magnusson, C.; Laurell, T., Acoustofluidics 8: Applications of acoustophoresis in continuous flow microsystems. Lab Chip 2012, 12 (7), 1210-1223. 81. Khandpur, R. S., Handbook of Biomedical Instrumentation. McGraw-Hill Professional: New Delhi, 2003. 82. Barnett, S. B.; Ter Haar, G. R.; Ziskin, M. C.; Rott, H.-D.; Duck, F. A.; Maeda, K., International recommendations and guidelines for the safe use of diagnostic ultrasound in medicine. Ultrasound in Medicine & Biology 2000, 26 (3), 355-366. 83. Bruus, H., Acoustofluidics 7: The acoustic radiation force on small particles. Lab Chip 2012, 12 (6), 1014-1021. 84. Syverton, J. T.; Scherer, W. F., Studies on the propagation in vitro of poliomyelitis viruses. I. Viral multiplications in tissue cultures employing monkey and human testicular cells. The Journal of experimental medicine 1952, 95 (5), 355-67. 85. Nichols, J. W.; Bae, Y. H., Odyssey of a cancer nanoparticle: From injection site to site of action. Nano Today 2012, 7 (6), 606-618. 86. Jain, R. K.; Stylianopoulos, T., Delivering nanomedicine to solid tumors. Nat Rev Clin Oncol 2010, 7 (11), 653-664. 87. Weiss, L.; Zeigel, R., Cell surface negativity and the binding of positively charged particles. J. Cell. Physiol. 1971, 77 (2), 179-185. 88. Solovev, A. A.; Xi, W.; Gracias, D. H.; Harazim, S. M.; Deneke, C.; Sanchez, S.; Schmidt, O. G., Self-Propelled Nanotools. ACS Nano 2012, 6 (2), 1751-1756. 89. Alkilany, A. M.; Murphy, C. J., Toxicity and cellular uptake of gold nanoparticles: what we have learned so far? J. Nanopart. Res. 2010, 12 (7), 2313-2333. 90. Albanese, A.; Tang, P. S.; Chan, W. C. W., The Effect of Nanoparticle Size, Shape, and Surface Chemistry on Biological Systems. Annu Rev Biomed Eng 2012, 14, 1-16.

91. Aderem, A.; Underhill, D. M., Mechanisms of phagocytosis in macrophages. Annu Rev Immunol 1999, 17, 593-623. 92. Hu, L.; Mao, Z. W.; Gao, C. Y., Colloidal particles for cellular uptake and delivery. J. Mater. Chem. 2009, 19 (20), 3108-3115. 93. Gratton, S. E. A.; Ropp, P. A.; Pohlhaus, P. D.; Luft, J. C.; Madden, V. J.; Napier, M. E.; DeSimone, J. M., The effect of particle design on cellular internalization pathways. P Natl Acad Sci USA 2008, 105 (33), 11613-11618. 94. Hauck, T. S.; Ghazani, A. A.; Chan, W. C., Assessing the effect of surface chemistry on gold nanorod uptake, toxicity, and gene expression in mammalian cells. Small 2008, 4 (1), 153-9.

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Chapter 5 Numerical modeling of self-electrophoretic motors with the COMSOL Multi-Physics program

5.1 Introduction

Among the research efforts in the field of nano- and micromotor systems, numerical modeling is a small yet important branch. It bridges theory and experiments, and provides a framework in which parameters can be tested and experimental results can be compared, in a way that is easily visualized. The goal of modeling is not necessarily to reproduce what has been observed experimentally, although that is sometimes the first step in testing the validity of a model and a foundation to build further features upon. Rather, models are established and developed to serve mainly as guidance to direct future exploration, as well to reveal details that are otherwise difficult to obtain experimentally. In this sense modeling and theory are equally important for further development of nano- and micromotors; the experimentalists can spend less time on inferior or faulty designs if they can be eliminated by well-informed modeling and theory.

A relatively small amount of the vast and growing literature on nano- and micromotors so far focuses on numerical modeling. There has been significant interest in developing numerical models for bimetallic nanomotors driven by self-electrophoresis. The effects of a number of parameters on the performance of bimetallic nanomotors have been studied. For example Zhang et al. used molecular dynamic simulations to study the effect of temperature and solvent concentration on the nanomotors, and discovered that both parameters would increase the motor speed in a non-linear fashion.1 Sabass and Seifert, on the other hand, studied the effect of the presence of salt in the solution on the behavior of bimetallic nanomotors by using numerical simulations, and the coupling between salt ion flux and the reaction-driven proton flux was found to be important.2 Notably numerical modeling was also used by Posner and coworkers in their

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simulation of bimetallic nanomotors in H2O2, which was very helpful in elucidating the mechanism of the propulsion.3, 4 Their model also agrees well with results obtained from experiments. Details of the Posner models will be presented and discussed in later sections.

Models of other nano- and micromotor systems have also been developed. A hybrid model based on molecular dynamics and mesoscopic multiparticle collisions (MD-MPC) has been extensively exploited by Kapral and coworkers to study a nano-dimer motor system consisting of one chemically active particle and one inert particle. These dimer particles were shown to be able to propel under appropriate conditions,5 and respond to external forces,6 fluid flows7 and chemical waves8 in interesting and dynamic ways. Collective behaviors of such dimers have also been simulated, and bound state pairs or swarming can occur under different conditions.9, 10 This dimer system can also be extended to systems of multiple particles, and polymers have been shown to be able to propel in similar fashion in the simulations.11

A number of other nano- and micromotor systems have been simulated in various modeling efforts. For example, metal clusters inside a carbon nanotube can perform thrusting motion, as was simulated by molecular dynamics.12 Osmophoresis of particles that release chemical species into the solution was studied by Brownian dynamics.13 Shi and coworkers studied the propulsion of nanoscale particles with catalytically active surfaces through molecular dynamics simulations.14, 15 Biological motors have also been modeled. This includes bacteria such as E Coli. which were shown to be able to collectively propel asymmetrically shaped gears.16

Enzymes show enhanced diffusion in and chemotaxis towards solutions of higher substrate concentration, as was simulated by a numerical modeling tool.17

Although Brownian dynamics and multiparticle collision dynamics are the favored simulation tools used by the majority of researchers in this field, the recent numerical models established with finite difference programs such as COMSOL by Posner et al. and Sen et al. have shown tremendous promise as simulation tools. COMSOL is a finite element software package that is capable of simultaneously solving multiple physics. Their ease of use, user-friendly

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interface and capability to correlate multiple physical effects and solve them simultaneously have made COMSOL an easy and powerful tool to use, especially for simulating nano- and micromotors moving in self-generated chemical gradients, where multiple phenomena such as chemical surface reactions, electric fields, and fluid mechanics need to be coupled and solved simultaneously.

5.2 Basic concepts and assumptions used in current COMSOL models

The current COMSOL model of the bimetallic motor system was developed by modifying the models used by Posner and coworkers.3, 4 In their models the motion of the bimetallic nanorods was attributed to an electrical body force that arises from the coupling between the electric field generated from the proton distribution and the charged solution around the nanorods. The proton distribution originates from a combination of proton generation at the anode and consumption at the cathode, and is further affected by the diffusion, convection and electrical migration of protons. The transport of ions is governed by the general flux equation:

where Ji is the flux of ion i and the three terms on the right represent convection, diffusion, and migration, respectively. Here u is the fluid velocity, is the electrostatic potential,

R is the gas constant, F is the Faraday constant, T is the temperature and ci, Di, zi are the concentration, diffusion coefficient and charge of species i, respectively.

The electric potential ϕ in Eqn. 5-1 is calculated using the Poisson equation:

where z+=1 and z-=-1, ρe is the volumetric charge density, F is the Faraday constant and

- c+ and c- are the concentration of the proton and the counter ion (HCO3 ), respectively.

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The fluid velocity is governed by incompressible Navier-Stokes equation:

where is the fluid density, is the pressure, and μ is the dynamic viscosity. gives the electrical body force.

This model agrees with experimental results well, and has served as the foundation of the current model. However there are a number of issues that should be noted for this model. First, in

Posner’s model it is not clear how the speed of motor is calculated, since C MS L is not capable of calculating particle speed in an electric field. Secondly, the simulation result from the Posner model shows an electric field distribution that is not straightforward and somewhat counter- intuitive. Thirdly although the Posner model is a comprehensive model which takes into account the surface electrochemical reaction and surface zeta potential, it is rather complicated and therefore can be challenging to understand.

The goal of the current work is to greatly simplify the Posner model without significantly sacrificing the accuracy of the results obtained from the simulation. In the modified version of this model, the framework to solve the proton distribution and the electric field in the Posner model is retained (Eqn. 5-1 and 5-2). However unlike their model, the propulsion of the bimetallic rods in this modified model is considered to be an electrophoretic effect in which the negatively charged rod is exposed to the electric field created by the proton gradient, and therefore moves forward due to simple electrophoretic motion. This is conceptually much easier to understand, and eliminates the electrical body force term ( ) in Eqn. 5-3. However since

COMSOL is not capable of simulating the electrophoretic motion of charged rod, simulation of the electro-osmotic flow around the nanorod was instead carried out. Not unlike the Posner model, the current model simulates the flow around the bimetallic rod caused by the coupling between the charged fluid layer next to the metal surface and the self-generated electric field. However this is achieved by taking advantage of the built-in electroosmotic wall boundary condition, circumventing the need for introducing an electroviscous force which has to be separately solved

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and therefore increases computational demand. The simulated electroosmotic flow velocity is then converted back to motor velocity following a simple algorithm (section 5.3).

Major assumptions of the current COMSOL model of bimetallic nanomotors are listed as follows:

1. The first dissociation of carbonic acid is considered to be the equilibrium that balances

- the concentration of protons and the counter ion C 3 , governed by the following equation:

Since the experiment was conducted without purging out CO2, the starting pH of the solution is close to 5.65, the equilibrium pH of water saturated with CO2. Therefore a bulk concentration of protons and bicarbonate ion can be calculated to be 2.24×10-6 mol/L each. This gives a more accurate simulation result than assuming a starting pH of 7 and an equilibrium between H+ and OH-.

2. As was adopted in ref. 3 and 4, we assume the flux at the electrode surface is uniform in the sense that the incoming or outgoing proton flux at the cathode and anode does not vary over time or location. It was found that such a simplification does not stray far from reality,4 and for our discussion it is considered sufficiently accurate.

3. The electro-osmotic fluid speed, not the motor speed, is simulated in the model, as was discussed above. This is equivalent to the scenario in which the motor (rod) is fixed and fluid around it moves, i.e. motor is acting as a micropump. The fluid speed u at each point, or the pumping speed is given by

Where is the zeta potential on the rod surface, is the permittivity of the medium (water), is the dynamic viscosity of water and E is the electric field, which is solved by using Eqn. 5.2 (E

= - ). The motor speed is related to the fluid (pump) speed simulated by COMSOL through a method developed by Solomentsev and Anderson.18 To put it simple, this method weights the

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effect of the fluid speed on the motor speed differently at different locations along the rod. This will be discussed in more detail in Chapter 5.3.

4. The thin double layer approximation was used to simulate the nanorod in 2 2. Therefore the intrinsic distribution of protons around the rod as a result of surface charge is not considered in calculating the final proton concentration profile. Instead the final proton concentration profile is created only by proton generation at the anode and consumption at the cathode. In addition the zeta potential on the rod surface does not contribute to the electric potential calculations.

5.3 Calculating motor speed based on the electroosmotic flow speed

The last aspect of the modeling is to calculate the motor speed based on the pumping speed obtained from the simulation. To convert the fluid speed to the speed of the nanomotor we used a technique developed by Solomentsehv and Anderson in 199418. In their paper the speed of a cylindrical particle in a non-uniform electric field was analytically solved to be:

〈 〉

〈 〉 where

〈 〉 ∫

⁄

is the speed of the nanomotor, is the fluid speed (pumping speed) at each point along the rod, is the radius of the rod and L is the characteristic length of the rod which is defined as half of the rod length. Parameter s is a function of the position on the cylinder that is defined as follows (s increases from -1 to 1 linearly):

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Figure 5-1. Illustration of the definition of s and L for a rod-shaped nanomotor.

This method essentially produces a weighed electrophoretic speed with the fluid velocity at different spots on the rod contributing differently to the overall motor speed. It tuned out that although near the center of the rod the fluid velocity is the largest, it has the least weight in the calculation of the overall motor speed. n the other hand, the “backward” fluid flow near the end of the rod as a result of proton flux out of the anode and into the cathode matters significantly more and therefore slows down the motor. Fig. 5-6 clearly illustrates the regular flow and backward flow around a bimetallic nanomotor. Fig. 5-2 shows the fluid speed distribution along the rod length and how the fluid speed affects the motor speed at each point (α/<α>).

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Figure 5-2. Fluid speed and its weight along the nanorod length. Fluid speed in the z direction was simulated by the C MS L 2D model. α/<α> was calculated for each point, and a higher

α/<α> value means a heavier weighting that the fluid speed carries at this point towards the final motor speed. The colored bimetallic rod is overlaid onto the figure for illustrative purpose.

Negative values of fluid speed indicate a flow direction from the anode to the cathode. The simulation was carried out on a nanomotor with a surface zeta potential of -50 mV and flux of

7×10-6 mol/(m2∙s). The motor speed is calculated to be 21.6 μm/s.

It is interesting to compare the numerical result of the motor speed obtained by the above technique with the speed estimated from the Smoluchowski equation. As was introduced previously, the distribution of protons around the Au-Pt nanorod results in a distribution of charges that leads to an electric field pointing from the anode (Pt) to the cathode (Au). If we assume that the electric field is uniformly distributed along the length of the rod as if the rod were exposed to an externally applied electric field, the magnitude of such an electric field can be

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roughly estimated from the difference of the electrical potential between the anode and cathode

( = 2.1 mV at a surface proton flux of 7×10-6 mol/(m2·s)) and the length of the rod (3 μm) to be 700 V/m. Knowing the electric field strength, the velocity of the electrophoretically transported Au-Pt nanorod can be estimated to be 24.8 μm/s by the Smoluchowski equation:

rod

where rod is the zeta potential of the bimetallic nanorod (~-50 mV, experimentally measured),

is the dielectric constant of water, is the viscosity and E is the electric field.

The Smoluchowski equation is widely used to estimate the speed of various nano/micromotors driven by electrophoretic/diffusiophoretic (the electrical component) mechanisms. 19-23 However in a system governed by the Smoluchowski equation, the electric field is normally applied externally, and thus locally it can be considered to be uniform. This is different from the case of self-electrophoretically or self-diffusiophoretically driven nano/micromotors where the electric field is self-generated and non-uniform. Therefore one might argue that the classic Smoluchowski equation can no longer give an accurate solution to the velocity of such a nano/micromotor. Yet the estimated motor speed with the Smoluchowski equation (24.8 μm/s) is fairly close to the motor speed calculated by the more rigorous method described above (21.6 μm/s), and does not stray far from experimental measured value (21 μm/s).

Therefore we believe that the Smoluchowski equation provides a convenient and relatively accurate way to estimate (at least the order of magnitude of) the electrophoretic velocity of charged particles in an electric field, even if the field is self-generated.

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5.4 Modeling details and results

5.4.1 Modeling details

COMSOL (version 4.2, provided by the Penn State Research Computer and

+ - Cyberinfrastructure (RCC) through remote access) was used to solve the H and HCO3 concentration distribution, the electric field and the pump speed. We used 2D simulations for rod- shaped catalytic bimetallic nanomotors. The Electrostatics module, Transport of Dilute Species module and Creeping Flow module were the physics used in building the models. In our 2D simulation, the metal rod is 3 μm in length and 300 nm in diameter. Gold and platinum segments are 1.5 μm long each. It is placed in a square of 100 μm on each side. The 2D model was set to be axially symmetric to simulate a cylindrical rod located at the center of a cylindrical volume of water (r-z coordinate system). This symmetry greatly reduces the computational demand. The remaining parameters needed in the models can be found in table 6.1, except for flux_in and D_in, which were used (see below) in the 3D modeling of tubular motors.

In the Transport of Dilute Species module, the cathode and anode proton flux on the rod surface was varied to reflect different concentrations of H2O2, and the flux were set to be equal in value but of opposite sign on the two ends of the motor to conserve mass and charge. A typical

-6 2 flux we used for the simulation was 7×10 mol/m ·s, which corresponds to 6% H2O2. The boundary condition for the four outside boundaries is set to be a constant proton bulk concentration. Convection and migration are further coupled to the other two modules by setting the velocity field to the solution from the Creeping flow module and the electric potential to the solution from the Electrostatic module, respectively.

In the Electrostatic module the initial value of the electric potential of the medium is set to be 0 V. The four outside boundaries are held at 0 potential at all times during the simulation.

The space charge density ( in Eqn. 5.2), which determines the electric potential and electric

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field distribution, is set as a variable that was defined under “definition” in the model (see Table

6.2)

In the Creeping Flow module the fluid needs to be set as imcompressible flow, and inertia should be automatically selected in this module to simulate the Stokes flow condition. The boundary conditions for the four outside walls are set to be open boundary (no viscous stress), and for the rod surface to be the electroosmotic velocity. The electric field is solved by the

Electrostatic module and the tangential electric field is used in the electroosmotic velocity boundary condition. The zeta potential of the metal rod is used (zeta_rod in Table 5.1) for

COMSOL to calculate the electroosmotic mobility. The top and bottom of the nanorod can be set to be no-slip for the sake of conserving computational power and facilitating convergence. These two surfaces will not contribute to the motion significantly.

Meshing is done by setting user-controlled mesh conditions. The general size is set to be calibrated for fluid hydrodynamics with a predefined finer mesh. A predefined fine mesh condition calibrated for fluid hydrodynamics is used for the fluid domain. It is very important to choose an appropriate meshing condition for the rod surface, and a good balance between accuracy and computation time can be achieved by meshing the surface with a maximum element size of 0.05 μm and a minimum size of 0.02 μm. Alternatively boundary layers can be used to create meshes for the rod surface. Free triangular mesh is used for all the meshing operations. The mesh generated by the above steps contains 8990 elements. A stationary simulation is carried out to calculate the motor system at steady state.

3D models were used to simulate tubular nanomotors because such shapes cannot be accurately represented with 2D axially symmetric models. The only differences between our 3D models and 2D models were that a smaller volume of water (a cube of 20 μm× 20 μm ×20 μm) and coarser mesh were used to decrease computational time. To study the effect of the reduced mass transfer of H2O2 into the tube, the proton flux of the inner surface was tuned to be 0.1, 0.2,

0.5 and 1 times of the flux on the outside (7×10-6 mol/m2·s). In the 3D simulation model, the tube

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motor has an inner diameter of 200 nm, with the outside diameter and the length the same as rod motors. These parameters are close to the actual dimensions of the fabricated nanotubes (See Fig.

2-5 in Chapter 2).

Although electroosmotic wall conditions can be used to calculate the fluid flow inside the tubular motors, numerous attempts have been carried out without successful convergence. One possible reason is that mesh is not fine enough to handle the complicated situation where electroosmotic flow on the inside surface overlaps when the tube inside diameter is essentially only of a few Debye lengths. Finer meshing exponentially increases the computational workload until it becomes impractical even for the servers through remote access. Therefore the fluid flow module has not been used in 3D models of tubular motors in order to conserve computational power and facilitate convergence. Nevertheless, since the emphasis of the simulation of a 3D tubular nanomotor is to examine the effect of proton trapping inside the tube, the results we obtained serve as a qualitative probe of the distribution of protons in a confined geometry and the performance of a tubular nanomotor.

5.4.2 Modeling results

In this section some typical results obtained from the simulation of bimetallic nanomotors are presented. These results are obtained with a surface flux of 7×10-6 mol/m2·s and a nanorod zeta potential of -50 mV, unless otherwise noted. The basic configuration of the 2D model system is illustrated in Fig. 5-3. The proton concentration profile, electric potential distribution and electric field distribution, and fluid flow of Au-Pt nanomotors simulated by 2D models are presented in Fig. 5-4 through 5-6, respectively. The effects of varying surface flux on the motor system are illustrated in Fig. 5-5, Fig. 5-6, Fig. 5-7 and Fig. 5-9.

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Figure 5-3. 2D model configuration of the bimetallic nanomotor system being simulated. The nanorod is placed in a square box of 100 μm on each side.

Figure 5-4. Proton concentration distribution of a Au-Pt nanomotor. Pt is at the top. Bottom axis: r coordinates in μm. Legend: Proton concentration in mol/m3.

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Figure 5-6. Electric potential profile of Au-Pt. Pt is on the top. Bottom axis: r coordinates in μm.

Color legend: Proton concentration in mol/m3.

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Figure 5-8. Fluid flow around a Au-Pt nanomotor. Color indicates the proton concentration, and arrows indicate the directions of the fluid flow. The length of the arrow is normalized and does not represent the flow magnitude. Pt is at the top. Bottom axis: r coordinates in μm. Color legend: proton concentration in mol/m3. Surface flux: 7×10-6 mol/(m2∙s)

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For 3D modeling of bimetallic tubular nanomotors, only the proton centration profile and the electric potential and electric field distribution are simulated. They are presented in Fig. 5-11 and 5-12. The model configuration is illustrated in Fig. 5-10.

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Figure 5-10. 3D model configuration of the tubular nanomotor system. Inset: blow-up of the tubular shape of the nanomotor used in the simulation.

Figure 5-11. y-z cut plane of the 3D simulation result of a tubular nanomotor showing the proton concentration profile inside and outside the tube. The flux inside the tube was set to be 1/10 of the

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outside flux to account for reduced mass transfer of H2O2 inside the tube. Both axis coordinates are in μm.

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Table 5-1. 2D and 3D modeling parameters

Parameters flux_out flux_in zeta_rod D_H C_H0 H_rod W_rod D_in Meaning Outside inside Zeta Diffusion Bulk proton Length of Diameter Tube inside Surface surface potential on coefficient of concentration each metal of the diameter flux flux the rod H+ segment metal rod Value 7e-6 7e-7 -0.05 9.31e-9 2.24e-3 1.5 0.3 0.2 Unit mol/(m2∙s) mol/(m2∙s) V m2/s mol/m3 μm μm μm

Table 5-2. Variables for COMSOL models

Variables c_HCO3 Rho_v - 3 Meaning concentration of HCO3 (in mol/ space charge density (ρ, in C/m ) m3) Expression 5.02e-6[mol2/m6]/c_H 96500[C/mol]*(c_H-c_HCO3)

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5.5 Conclusions

COMSOL modeling of bimetallic nanorods has proven to be an easy and powerful tool.

The computational time is usually short thanks to the axial symmetry of the nanorod, and can be further reduced by using 2D models. Yet it is capable of providing detailed information on many aspects of the motors that are otherwise difficult or even impossible to measure. The information directly available from the simulations includes concentration profiles of chemical species involved, electric potential distributions and the resulting electric field, and electroosmotic flow magnitudes and directions. In addition COMSOL can also provide information about the relative magnitudes of diffusion, electrical migration and convection of the chemical species, which become important in understanding the maintenance of the proton gradient. Furthermore, by cutting 2D planes or 1D lines along various directions, quantitative information becomes available that greatly benefits analysis. Although 3D modeling of tubular shaped bimetallic catalytic nanomotors has revealed interesting details about proton confinement inside the tube, its true potential can only be harnessed by choosing the appropriate combinations of dimensions and meshing conditions, which await further studies.

The power of modeling also manifests itself in that multiple values can be simulated at the same time for one particular variable (parameter sweep), generating results that can be compared in parallel. This is especially useful for studying the effect of varying the surface flux, rod dimensions or surface zeta potential on the motor behaviors. Through the use of parameter sweeps, it has been demonstrated that the motor speed increases linearly with increasing surface flux and surface zeta potential.

Finally, it is very important to recognize that modeling can be a misleading tool if improperly used. Finite element modeling has a gullible nature; it trusts user input and loyally

121 computes. There is no way for the modeling tool to tell if a certain condition is correct or if the generated result is meaningful. That responsibility ultimately lies with the user. Therefore great caution is needed to interpret any simulation result, and any direct comparison between simulation and experimental results has to be carried out critically. Unfortunately finite element simulation tools are not commonly used by experimentalists, and as a result only limited literature exists to bridge experiments with simulation coherently. It is my sincere hope that future generations of researchers can take full advantage of the power of finite element simulations, but without being misled by results that do not accurately represent the physics because of limitations in the model, or because the simulations are not carefully interpreted.

5.6 References

1. Zhang, G.; Sun, Q.; Li, L.; Wang, L., The Effect of Temperature and Solvent Concentration on the Nanomotor Motion by Molecular Dynamics Simulation. Applied Mechanics and Materials 2012, 190-191, 253-256. 2. Sabass, B.; Seifert, U., Nonlinear, electrocatalytic swimming in the presence of salt. J. Chem. Phys. 2012, 136 (21). 3. Moran, J.; Wheat, P.; Posner, J., Locomotion of electrocatalytic nanomotors due to reaction induced charge autoelectrophoresis. Phys Rev E 2010, 81 (6). 4. Moran, J. L.; Posner, J. D., Electrokinetic locomotion due to reaction-induced charge auto-electrophoresis. Journal of Fluid Mechanics 2011, 680, 31-66. 5. Ruckner, G.; Kapral, R., Chemically powered nanodimers. Phys. Rev. Lett. 2007, 98 (15). 6. Tao, Y. G.; Kapral, R., Dynamics of chemically powered nanodimer motors subject to an external force. J. Chem. Phys. 2009, 131 (2). 7. Tao, Y. G.; Kapral, R., Swimming upstream: self-propelled nanodimer motors in a flow. Soft Matter 2010, 6 (4), 756-761. 8. Thakur, S.; Chen, J. X.; Kapral, R., Interaction of a Chemically Propelled Nanomotor with a Chemical Wave. Angew Chem Int Edit 2011, 50 (43), 10165-10169. 9. Thakur, S.; Kapral, R., Self-propelled nanodimer bound state pairs. J. Chem. Phys. 2010, 133 (20). 10. Thakur, S.; Kapral, R., Collective dynamics of self-propelled sphere-dimer motors. Phys Rev E 2012, 85 (2). 11. Tao, Y. G.; Kapral, R., Self-Propelled Polymer Nanomotors. Chemphyschem 2009, 10 (5), 770-773.

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12. Delogu, F., Self-Propulsion of Capped Carbon Nanotubes: A Molecular Dynamics Study. J Phys Chem C 2010, 114 (21), 9664-9671. 13. Cordova-Figueroa, U. M.; Brady, J. F., Osmotic propulsion: The osmotic motor. Phys. Rev. Lett. 2008, 100 (15). 14. Shi, Y. F.; Huang, L. P.; Brenner, D. W., Computational study of nanometer-scale self- propulsion enabled by asymmetric chemical catalysis. J. Chem. Phys. 2009, 131 (1). 15. Chen, Y. P.; Shi, Y. F., Characterizing the Autonomous Motions of Linear Catalytic Nanomotors Using Molecular Dynamics Simulations. J Phys Chem C 2011, 115 (40), 19588- 19597. 16. Angelani, L.; Di Leonardo, R.; Ruocco, G., Self-Starting Micromotors in a Bacterial Bath. Phys. Rev. Lett. 2009, 102 (4). 17. Sengupta, S.; Dey, K. K.; Muddana, H. S.; Tabouillot, T.; Ibele, M. E.; Butler, P. J.; Sen, A., Enzyme Molecules as Nanomotors. J. Am. Chem. Soc. 2013, 135 (4), 1406-1414. 18. Solomentsev, Y.; Anderson, J. L., Electrophoresis of slender particles. J. Fluid Mech. 1994, 279, 197-215. 19. Kazoe, Y.; Yoda, M., Experimental Study of the Effect of External Electric Fields on Interfacial Dynamics of Colloidal Particles. Langmuir 2011, 27 (18), 11481-11488. 20. Paxton, W. F.; Baker, P. T.; Kline, T. R.; Wang, Y.; Mallouk, T. E.; Sen, A., Catalytically induced electrokinetics for motors and micropumps. J Am Chem Soc 2006, 128 (46), 14881-14888. 21. Kline, T. R.; Iwata, J.; Lammert, P. E.; Mallouk, T. E.; Sen, A.; Velegol, D., Catalytically driven colloidal patterning and transport. J Phys Chem B 2006, 110 (48), 24513-21. 22. Paxton, W. F.; Sen, A.; Mallouk, T. E., Motility of catalytic nanoparticles through self- generated forces. Chemistry-a European Journal 2005, 11 (22), 6462-6470. 23. Chang, S. T.; Paunov, V. N.; Petsev, D. N.; Velev, O. D., Remotely powered self- propelling particles and micropumps based on miniature diodes. Nat Mater 2007, 6 (3), 235-40.

123 VITA

Wei Wang Mallouk group, Department of Chemistry Tel: (814)-308-4038 Pennsylvania State University email: [email protected] 104 Chemistry Building University Park, PA 16802

Research interests Solid state chemistry; Nanoscale inorganic materials; Computational simulation of materials; Colloidal science; Nano- and micromotors; 1D and 2D materials synthesis; Electrochemistry; Electrodeposition

Education 2008-present the Pennsylvania State University (Penn State), State College, PA, U.S.A • Ph.D. candidate in chemistry. Advisor: Thomas Mallouk, Evan Pugh professor 2004-2008 Harbin Institute of Technology (HIT), Harbin, Heilongjiang, P.R.China • B.S. in applied chemistry. Advisor: Prof. Sue ao Publication

1. Wang, W.; Castro, L. A.; oyos, M.; Mallouk, T. E, “Autonomous motion of metallic micro-rods propelled by ultrasound,” ACS Nano, 2012, 6(7), 6122-6132 2. Wang, W.; Chiang, T.-Y.; Velegol, D.; Mallouk, T. E., Understanding the Efficiency of Autonomous Nano- and Microscale Motors. JACS, accepted 3. Wang, W.; Duan, W.; Sen, A.; Mallouk, T.E., Autonomous assemblers: catalytically powered dynamic assembly of rod-shaped nanomotors and passive tracer particles. Submitted

4. E. A. ernandez-Pagan, W. Wang, and T. E. Mallouk, “Template Electrodeposition of

Single-Phase p- and n-Type Copper Indium Diselenide (CuInSe2) Nanowire Arrays,” ACS Nano 2011, 5, 3237-3241. 5. Y. Chen, X. Ding, S.-C. S. Lin, S. Yang, P.- . uang, N. Nama, Y. Zhao, A. A. Nawaz, F. Guo, W. Wang, T. E. Mallouk, and T. J. uang, "Tunable nanowire patterning using standing surface acoustic waves (SSAW)”, ACS Nano, 2013, 7(4), 3306-3314